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How can you prove in at least two ways that the straight line of y equals 2x plus 5 over 4 is a tangent to the curve of y square equals 10x?
Wiki User
∙ 13y ago
Combine the two equations together to give a quadratic equation in the form of:-
4x2 - 5x + 25/16 = 0
The solution to this is x = 5/8 or x = 5/8 meaning that it has equal roots therefore the line is tangent to the curve.
The discriminant of b2 - 4ac = 0 also proves that the quadratic equation has two equal roots which makes the line tangent to the curve.
Further proof can be found by plotting the straight line and curve graphically.
Wiki User
∙ 13y ago
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Straight lines that touch but don't intersect a curve?
Tangent to the curve.
What is the name given to a straight line that touches a curve?
In geometry a straight line that touches a curve is called a tangent.
In maths what is a tangent and what is a chord?
Tangent:In geometry, the tangent line (or simply the tangent) is a curve at a given point and is the straight line that "just touches" the curve at that point. As it passes through the point where the tangent line and the curve meet the tangent line is "going in the same direction" as the curve, and in this sense it is the best straight-line approximation to the curve at that point.Chord:A chord of a curve is a geometric line segment whose endpoints both lie on the outside of the circle.
What is the definition of a tangent line?
A tangent is a line that just touches a curve at a single point and its gradient equals the rate of change of the curve at that point.
What t-word is define in geometry as a straight line that touches a curve but continues on with crossing it?
A tangent line touches a curve or the circumference of a circle at just one point.
What is a straight line that touches a curve but continues on with crossing it?
A tangent line.
What is meant by tangent to a curve at a point?
It is a straight line that touches the curve such that the line is perpendicular to the radius of the curve at the point of contact.
Is tangent in geometry and tangent in trigonometry same?
Yes a tangent is a straight line thattouches a curve at only one point But there is a tangent ratio used in trigonometry
What is the antonym of tangent?
The answer depends on the context. In the context of a curve, a tangent is a straight line that touches the line without intersecting it. The antonym does not have a specific name because it could be a straight line that does not meet the curve at all, or it could be one that crosses the curve. Note that even a tangent can cross the curve at some other [distant] point(s).
What t-word is defined in geometry as a straight line that touches a curve?
tangent
What is a straight line or plane that touches a curve or curved surface at one point?
A tangent
Do a straight line and a curved line form avertex at its joining point?
A tangent at that point where a straight line just touches a curve and a secant line when the straight line bisects the curve.
