Question

If the axes of an ellipse coincide with the co-ordinate axes and it passes through the point $(4,-1)$ and touches the line $x+4y-10=0$ then its equation is

• A. $\frac{x^2}{80}+\frac{y^2}{5/4}=1$
• B. $\frac{x^2}{5/4}+\frac{y^2}{20}=1$
• C. $\frac{x^2}{25}+\frac{3y^2}{5}=1$
• D. $\frac{x^2}{20}+\frac{y^2}{5}=1$

Answer 1

Answer: (A)

$\frac{x^2}{80}+\frac{y^2}{5/4}=1$

let the equation of ellipse be

$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$

comparing $y=mx\pm \sqrt{a^2{m}^2+b^2}$ with the given line

$\frac{a^2}{16}+b^2=\frac{100}{16}$

& putting $(4,1)$ in the equation

$\frac{16}{a^2}+\frac{1}{b^2}=1$

$\therefore a^2=80b^2=5/4$

$\therefore$ Option A ia correct