Question

If $x=asin\theta ,y=btan\theta ,$ then

• A. $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$
• B. $\frac{a^2}{x^2}+\frac{b^2}{y^2}=1$
• C. $\frac{a^2}{x^2}-\frac{b^2}{y^2}=1$
• D. $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$

Answer 1

The correct option is C $\frac{a^2}{x^2}-\frac{b^2}{y^2}=1$

Substituting the values of x and y in the third option:
$\frac{a^2}{a^2{\sin }^2\theta }-\frac{b^2}{b^2{\tan }^2\theta }=\frac{1}{{\sin }^2\theta }-\frac{1}{{\tan }^2\theta }=\frac{1-{\cos }^2\theta }{{\sin }^2\theta }=\frac{{\sin }^2\theta }{{\sin }^2\theta }=1$