Consider the following. x = tan^2(θ), y = sec(θ), −π/2 < θ < π/2 Eliminate the parameter to find a Cartesian equation of the curve

Question

I believe I messed up somewhere along the way. I solved this as cosθ= 1/y and substituted into x to get x=sin^2(θ)/(1/y)^2. Simplifying to get x=y times sinθ. The website that our homework is through says this is incorrect. Any help is offered.

Answer 1

You are almost there, you have to exclude θ completely and have an equation that contains only x and y

this is correct x=sin²(θ)/y².

Now think how to get rid of sin²(θ).

 Since

x = tan²(θ), y = sec(θ), I would do this:

x-y²=tan²(θ)- sec²(θ) = sin²(θ)/cos²(θ)-1/cos²(θ) =

= (sin²(θ)-1)/cos²(θ)=-1

So the equation will be

y²=x+1

Check the condition −π/2 < θ < π/2 yourself