Question

What conic section is drawn by the parametric equations x=csc t and y cot?

A. Parabola

B. Circle

C. Ellipse

D. Hyperbola

Answer 1

If we take the square of x and square of y and then subtract them:
(csc t)²-(cot t)²=1 ( this eq. gets from basic identity
x²-y²=1......a 1+cot²x=csc²x)

equation 'a' represent the equation of hyperbola which is (x²/a²)-(y²/b²) =1 with given conditions( a=1,b=1)

So, option D is correct