Question

An ellipse with foci $(-1,1)$ and $(1,1)$ passes through $(0,0)$ then its equation is?

• A. $x^2+2y^2-8y=0$
• B. $x^2+2y^2+4y=0$
• C. $x^2+2y^2+8y=0$
• D. $x^2+2y^2-4y=0$

Answer 1

The correct option is D $x^2+2y^2-4y=0$

Foci $(-1,1)$ & $(1,1)$ of ellipse.

Passes through $(0,0)$

Centre of ellipse $=(0,1)$ midpoints of the line between focus

value $b=1$

$ae=1$

$a\sqrt{1-\frac{b^2}{a^2}}\Rightarrow a\sqrt{1-\frac{1}{a^2}}=1\Rightarrow \sqrt{a^2-1}=1$

$a=\sqrt{2}$

centre is shifted to $(0,1)$.

$\frac{(x-0{)}^2}{(\sqrt{2}{)}^2}+\frac{(y-1{)}^2}{1}=1$

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

$x^2+2y^2+2-4y=2$

$x^2+2y^2-4y=0$

option $D$ is correct.