Eliminate `theta` from the equation `a=x sec theta and b=y tan theta `.

Explanation

We know that trigonmetric ratios are meaningful when they are associated with some `theta` , i.e., we cannot imagine any trigonometric ratio without `theta`. Eliminate `theta` means, eliminating the trigonometric ratios by using suitable identity.
Given , `a=x sec theta and b=y tan theta `
`(a)/(x) =sec theta and (b)/(y)=tan theta `
We know that `, sec^(2) theta-tan^(2) theta=1`.
So,`((a)/(x))^(2)=((b)/(y))^(2)=1`
`(a^(2))/(x^(2))-(b^(2))/(y^(2))=1`.
Hence, the required equation is `(a^(2))/(x^(2))-(b^(2))/(y^(2))=1`.