The curve $C$ has parametric equations $x=5\alpha \sec heta $, $y=3\alpha an heta $, where $-\

Question

The curve $C$ has parametric equations $x=5\alpha \sec 	heta $, $y=3\alpha 	an 	heta $, where $-\frac{\pi }{2}and $\alpha $ is a positive constant. Find the cartesian equation of $C$. [2] Sketch $C$, giving the coordinates of any points of intersection with the axes and the equations of any asymptotes. [3] Determine the range of values of $k$ such that the line $ky=x$ meets the curve $C$. [2]

Accepted Answer

(i) $\frac{x^2}{25\alpha^2} - \frac{y^2}{9\alpha^2} = 1$, (iii) $k \frac{5}{3}$

2022 NYJC J1 CT Q4

2022 NYJC J1 CT Q4

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