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What is the distance from a point on the x axis to the centre of the circle x2 plus y2 -2x -6y plus 5 equals 0 from the same point where a tangent line meets the circle at 3 4?
Wiki User
∙ 6y ago
Equation of circle: x^2 +y^2 -2x -6y +5 = 0
Completing the squares: (x -1)^2 +(y -3)^2 = 5 which is radius squared
Center of circle: (1, 3)
Tangent line is at right angles to the radius at (3, 4) and meets the x axis at (5, 0)
Distance from point (5, 0) to center of circle (1, 3) = 5 units using distance formula
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∙ 6y ago
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What is the distance to the center of the circle x2 plus y2 -2x -6y plus 5 equals 0 from the x axis at the same point when the tangent line meets the x axis from the point 3 4?
Equation of circle: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 = 5 Center of circle: (1, 3) Tangent line from (3, 4) meets the x axis at: (5, 0) Distance from (5, 0) to (1, 3) = 5 using the distance formula
What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
What is the chord that passes through the centre of a circle?
The chord that passes through the center of a circle is called the diameter. The measure of this chord is also called the diameter, and is used in calculations such as finding the circumference of a circle (Circumference equals pi times the diameter).^^wrong...it is eitherSecant or tangent im pretty sure its SECANT though...
What is the length of the tangent line from the point 8 2 to a point where it touches the circle of x2 plus y2 -4x -8y -5 equals 0 on the Cartesian plane?
The distance from (8, 2) to the center of the circle forms the hypotenuse of a right angle triangle with the circle's radius meeting the tangent line at right angles and so:- Equation of the circle: x^2 +y^2 -4x -8y -5 = 0 Completing the squares: (x-2)^2 +(y-4)^2 = 25 Center of circle: (2, 4) Radius of circle: 5 Distance from (8, 2) to (2, 4): 2 times square root of 10 Using Pythagoras' theorem: distance squared minus radius squared = 15 Therefore length of the tangent line is the square root of 15
What is the length of the tangent line from the origin to a point where it touches the circle x2 plus y2 plus 4x minus 6y plus 10 equals 0 on the Cartesian plane?
The tangent of a circle is perpendicular to the radius to the point of contact (Xc, Yc).The point (0, 0), the centre of the circle (Xo, Yo) and the point of contact of the tangent (Xc, Yc) form a right angle triangle.The leg from the point (0, 0) to the point of contact (Xc, Yc) is the required lengthThe leg from the centre of the circle (Xo, Yo) to the point of contact (Xc, Yc) has length equal to the radius (r) of the circleThe hypotenuse is the length between the point (0, 0) and the centre of the circle (Xo, Yo).To solve this:Find the centre (Xo, Yo) of the circle, and its radius r.Use Pythagoras to find the length between the point (0, 0) and the centre of the circle (Xo, Yo)Use Pythagoras to find the length between the point (0, 0) and the point of contact (Xc, Yc) of the tangent - the required length.Hint: a circle with centre (Xo, Yo) and radius r has an equation of the form:(x - Xo)² + (y - Yo)² = r²Have a go at solving it now you know how, before reading the solution below:------------------------------------------------------------------------------Circle:x² + y² + 4x - 6y + 10 = 0→ x² + 4x + y² - 6y + 10 = 0→ (x + (4/2))² - (4/2)² + (y + (-6/2))² - (-6/2)² +10 = 0→ (x + 2)² - 4 + (y - 3)² - 9 + 10 = 0→ (x + 2)² + (y - 3)² = 3 = radius²→ Circle has centre (-2, 3) and radius √3Line from centre of circle (-2, 3) to the given point (0, 0):Using Pythagoras to find length of a line between two points (x1, y1) and (x2, y2):length = √((x2 - x1)² + (y2 - y1)²)To find length between given point (0, 0) and centre of circle (-2, 3)→ length = √((0 - -2)² + (0 - 3)²)= √(2² + (-3)²)= √13Tangent line segment:Using Pythagoras to find length of tangent between point (0, 0) and its point of contact with the circle:centre_to_point² = tangent² + radius²→ tangent = √(centre_to_point² - radius²)= √((√13)² + (√3)²)= √(13 + 3)= √16= 4
What is the distance to the center of the circle x2 plus y2 -2x -6y plus 5 equals 0 from the x axis at the same point when the tangent line meets the x axis from the point 3 4?
Equation of circle: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 = 5 Center of circle: (1, 3) Tangent line from (3, 4) meets the x axis at: (5, 0) Distance from (5, 0) to (1, 3) = 5 using the distance formula
What is the distance from a point on the x axis to the centre of a circle when a tangent line at the point 3 4 meets the circle of x2 plus y2 -2x -6y plus 5 equals 0?
Circle equation: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 = 5 Centre of circle: (1, 3) Tangent line meets the x-axis at: (0, 5) Distance from (0, 5) to (1, 3) = 5 units using the distance formula
What is the distance from a defined point on the x axis to the centre of circle x2 plus y2 -2x -6y plus 5 equals 0 when its tangent is at 3 4 on the Cartesian plane?
Equation of circle: x^2 +y^2 -2x -6y +5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 = 5 Center of circle: (1, 3) Tangent contact point: (3, 4) Slope of radius: ((3-4)/(1-3) = 1/2 Slope of tangent line: -2 Equation of tangent line: y-4 = -2(x-3) => y = -2x+10 Equation tangent rearranged: 2x+y = 10 When y equals 0 then x = 5 or (5, 0) as a coordinate Distance from (5, 0) to (1, 3) = 5 using the distance formula
What is the distance from the centre of a circle to a point on the x axis that forms a tangent line when it meets the circle of x2 plus y2 -2x -6y plus 5 equals 0 at the point 3 and 4?
Point of contact: (3, 4) Circle equation: x^2 +y^2 -2x -6y+5 = 0 Completing the squares: (x-1)^2 +(y-3)^2 -1 -9 +5 = 0 So: (x-1)^2 +(y-3) = 5 Centre of circle: (1, 3) Slope of radius: (3-4)/(1-3) = 1/2 Slope of tangent: -2 Equation of tangent line: y-4 = -2(x-3) => 2x+y = 10 Tangent line meets the x axis at: (5, 0) Using formula distance from (1, 3) to (5, 0) = 5 units
What is the distance from a point on the x axis to the center of the circle x2 plus y2 -2x -6y plus 5 equals 0 when the tangent of the circle is at 3 4?
If I understand your question you are asking for the distance from the point of intersection of the x-axis and the tangent to the circle at (3, 4) to the centre of the circle.To solve this you need to:Find the centre of the circle (X, Y) - a circle with equation (x - X)² + (y - Y)² = r² has a centre of (X, Y) and radius r;Find the slope m of the radius from the centre of the circle and the point of contact of the tangent;Use the slope m of the radius to calculate the slope m' of the tangent - the slopes of two perpendicular lines is such that mm' = -1;Use the slope-point equation of a line to find the equation of the tangent - a line with slope m through point (X, Y) has equation: y - Y = m(x - X);Find the point where this line crosses the x-axisUse Pythagoras to find the distance from this point to the centre of the circle.Have a go before reading the solution belowHint: You need to complete the squares in x and y to rearrange the equation for the circle into the form in step 1.---------------------------------------------------------------------1. Find the centre of the circle x² + y² - 2x - 6y + 5 = 0x² + y² - 2x - 6y + 5 = 0→ x² - 2x + y² - 6y + 5 = 0→ (x - 2/2)² - (2/2)² + (y - 6/2)² - (6/2)² + 5 = 0→ (x - 1)² - 1 + (y - 3)² - 9 + 5 = 0→ (x - 1)² + (y - 3)² = 5→ centre of circle is at (1, 3)2. Find the slope of the radius to (3, 4)slope = change_in_y/change_in_x→ m = (4 - 3)/ (3 - 1)= 1/23. Calculate the slope of the tangentmm' = -1→ m' = -1/m= -1(1/2)= -2→ slope of tangent is -24. Find the equation of the tangenty - 4 = -2(x - 3)→ y - 4 = -2x + 6→ y + 2x = 105. Find the point where the tangent crosses the x-axisx-axis is the line y = 0→ y + 2x = 10→ 0 + 2x = 10→ 2x = 10→ x = 5→ tangent crosses x-axis at (5, 0)6. Find the distance using Pythagorasdistance = √(difference_in_x² + difference_in_y²)= √((5 - 1)² + (3 - 0)²)= √(4² + 3²)= √(16 + 9)= √25= 5→ The distance from the intersection of the x-axis and the tangent to the circle x² + y² - 2x - 6y + 5 = 0 at (3, 4) to the centre of that circle is 5 units.
What is the radius equation inside the circle x squared plus y squared -8x plus 4y equals 30 that meets the tangent line y equals x plus 4 on the Cartesian plane showing work?
Circle equation: x^2 +y^2 -8x +4y = 30 Tangent line equation: y = x+4 Centre of circle: (4, -2) Slope of radius: -1 Radius equation: y--2 = -1(x-4) => y = -x+2 Note that this proves that tangent of a circle is always at right angles to its radius
What is the equation of the tangent line that touches the circle x squared plus y squared -8x -16y -209 equals 0 at a coordinate of 21 and 8?
Circle equation: x^2 +y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) Radius of circle 17 Slope of radius: 0 Perpendicular tangent slope: 0 Tangent point of contact: (21, 8) Tangent equation: x = 21 passing through (21, 0)
What is the tangent equation that touches the circle x2 -y2 -8x -16y -209 equals 0 at the point of 21 and 8 on the Cartesian plane?
Point of contact: (21, 8) Equation of circle: x^2 -y^2 -8x -16y -209 = 0 Completing the squares: (x-4)^2 +(y-8)^2 = 289 Centre of circle: (4, 8) and its radius is 17 Slope of radius: 0 Slope of tangent: 0 Tangent equation of the circle: x = 21 meaning that the tangent line is parallel to the y axis and that the radius is parallel to the x axis.
What is the length of a tangent line from the point 7 -2 to a point when it touches the circle x2 plus y2 -10 equals 49?
x² + y² - 10 = 49 → x² + y² = 59 = (x - 0)² + (y - 0)² = (√59)² → circle has centre (0, 0) - the origin - and radius √59 The point (7, -2) has a distance from the centre of the circle of: √((7 - 0)² + (-2 - 0)²) = √(7² + (-2)²) = √(49 + 4) = √53 < √59 Which means that the point is INSIDE the circle and all lines drawn from it to a point on the circumference will NOT be a tangent - the lines will CROSS the circumference, not touch it. Thus there is no solution to the problem as posed. -------------------------------------------------------------------- If the equation for the circle is wrong (which is most likely given as how it was stated) please re-submit your question with the correct equation for the circle.
What is the length of the tangent line from the origin when it meets the circle of x2 plus y2 plus 4x -6y plus 10 equals 0?
A circle with centre (X, Y) and radius r has an equation of the form: (x - X)² + (y - Y)² = r² Completing the square in x and y for the given equation gives: x² + y² + 4x - 6y + 10 = 0 → (x + (4/2))² - (4/2)² + (y - 6/2) - (6/2)² + 10 = 0 → (x + 2)² +(y - 3)² -2² - 3² + 10 = 0 → (x - -2)² + (y - 3)² = 4 + 9 - 10 = 3 → centre of circle is (-2, 3) and radius is √3 Where a tangent meets a circle it forms a right angle with a radius of the circle. Thus the origin, point of contact of tangent and centre of the circle form a right angled triangle with the hypotenuse the side between the origin and the centre of the circle. Thus Pythagoras can be used to find the length of the hypotenuse and the tangent: tangent² + radius² = hypotenuse² → tangent = √(hypotenuse² - radius²) = √((-2 - 0)² + (3 - 0)² - 3) = √((-2)² + (3)² - 3) = √(4 + 9 - 3) = √10 units ≈ 3.16 units
What is the chord that passes through the centre of a circle?
The chord that passes through the center of a circle is called the diameter. The measure of this chord is also called the diameter, and is used in calculations such as finding the circumference of a circle (Circumference equals pi times the diameter).^^wrong...it is eitherSecant or tangent im pretty sure its SECANT though...
What is the tangent equation of the circle x2 plus 6 plus y2 -10 equals 0 when it passes through 0 0 on the Cartesian plane?
Circle passing through coordinate: (0, 0) Circle equation: x^2 +6 +y^2 -10 = 0 Completing the squares: (x+3)^2 +(y-5)^2 = 34 Centre of circle: (-3, 5) Slope of radius: -5/3 Slope of tangent: 3/5 Tangent equation: y-0 = 3/5(x-0) => y = 3/5x
