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I have been given the question of:

A curve has the parametric equations x=2$t^2$ and y=4t. Find the value(s) of k if y=x+k is a tangent to the curve.

Being the first question I've gotten of this nature I have no idea on how to go about it.

loubloom
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  • Welcome to MSE. Your question is phrased as an isolated problem, without any further information or context. This does not match many users' quality standards, so it may attract downvotes, or closed. To prevent that, please [edit] the question. This will help you recognise and resolve the issues. Concretely: please provide context, and include your work and thoughts on the problem. These changes can help in formulating more appropriate answers. – José Carlos Santos Jan 13 '21 at 08:08

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So first find cartesian equation of parametric equation: y=4t so y^2=16t^2 then y^2/x=8 so x=y^2/8. also y=x+k so x=y-k. now y^2/8=y-k so y^2-8y+8k=0. it is clear we want one solution for y or else the line will intersect at more than one point and not be tangent. so discriminant =0, (-8)^2-32k=0 so k=2. Final answer y=x+2 only one solutionenter image description here

Aiden Chow
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