Question

Foci $(0,1),(0,-1)$ and the length of minor axis is $1.$ If the equation of ellipse is $p{x}^2+q{y}^2=5$. Find the value of $p+q$.

• A. $22$
• B. $24$
• C. $25$
• D. $26$

Answer 1

The correct option is B $24$

Foci lie on y-axis so that the equation of the ellipse is of the form $\frac{x^2}{b^2}+\frac{y^2}{a^2}=1$
where $a^2>b^2.$
Again distance between foci $=2ae=2$, (given) $\therefore ae=1$
Also $2b=1$ (given) $\therefore b=\frac{1}{2}$
And we know $b^2=a^2-a^2{e}^2$ or $\frac{1}{4}=a^2-1$
or $a^2=\frac{5}{4}$
Hence the equation of the ellipse is $\frac{x^2}{1/4}+\frac{y^2}{5/4}=1$
or $4x^2+\frac{4}{5}{y}^2=1\Rightarrow 20x^2+4y^2=5$