Please solve my problem

Question

I I have attached the Google Drive link. In this link, have uploaded image of the question please open it and solve my problem because I cannot upload the image here thank you

https://drive.google.com/file/d/1cU-PbZJQk60quQH2bS6uffLa9GxU7eCl/view?usp=drivesdk

Answer 1

Hint: the tangent of theta is equal to the slope of the curve at point (x,y).

Step 1. Use this to write an equation relating x to tan(theta).

Step 2. Solve for x as a function x(theta).

Step 3. Write the parameterization as (x(theta),y(theta)) = (x(theta),sqrt(x(theta))).

Answer 2

tan θ = y /x

tan θ = √x /x ⇒ cot θ = √x. ⇒ x = cot²θ

Then r (θ ) = < cot²θ , cot θ > , θ ∈ ( 0, π / 2]