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What is the point of contact when the line x -2y plus 12 equals 0 touches the circle x2 plus y2 -x -31 equals 0?
Wiki User
∙ 6y ago
If: x-2y+12 = 0 then x = 2y-12 or x^2 = (2y-12)^2
If: x^2+y^2 -x -31 = 0 then (2y-12)^2 +y2 -(2y-12)-31
Expanding brackets: 4y^2 -48y +144+y^2 -2y+12-31 = 0
Collecting like terms: 5y^2 -50y+125 = 0
Divide all terms by 5: y^2 -10y+25 = 0
Factorizing the above quadratic equation: (y-5)(y-5) = 0 meaning y =5
Therefore by substitution point of contact is made at: (-2, 5) and that the line is a tangent to the circle.
Wiki User
∙ 6y ago
Wiki User
∙ 6y agoThe point is (-2, 5).
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Tangent of a circle is what?
A tangent of a circle is a straight line that touches the circle at only one point.
What is the point of contact when the tangent line y -3x -5 equals 0 touches the circle x2 plus y2 -2x plus 4y -5 equals 0?
It works out that the tangent line of y -3x -5 = 0 makes contact with the circle x^2 +y^2 -2x +4y -5 = 0 at the coordinate of (-2, -1) on the coordinated grid.
Definition of tangent in a circle?
A tangent to a circle is a line from a point outside the circles which touches the circle at a single point.
A line that touches the circle at one point?
the answer is a Tangent.
The point where the tangent line intersects a circle?
A tangent line touches the circumference of a circle at just one point but it does not intersect the circle.
What is the point of contact when the line y equals 2x plus 1.25 touches the curve y squared equals 10x?
Combine the equations together and using the quadratic equation formula it works out that the point of contact is at (5/8, 5/2)
What is the tangent of a circle?
A tangent is a straight line that touches a circle's circumference at one point
How do you find the tangent of a circle?
a tangent is a line that touches the circle at only ONE point
What is the tangency of a circle?
A tangent of a circle is a straight line that touches the circle's circumference at just one point
What is a line that touches a circle in only one point?
A tangent.
What is the equation of the circle that touches the x axis when its center is at 2 5?
Center of circle: (2, 5) Point of contact with the x axis: (2, 0) Distance from (2, 5) to (2, 0) equals 5 which is the radius of the circle Equation of the circle: (x-2)^2 +(y-5)^2 = 25
How can you recognize a tangent of a circle?
A tangent of a circle is a straight line that touches the circle's circumference at just one point.
