Question

Find the equation of the ellipse with centre at $(-2,3)$, with a minor axis of $4$, parallel to the $x$-axis and a major axis of $6$, parallel to the $y$-axis.

• A. $\frac{(x-2{)}^2}{4}+\frac{(y-3{)}^2}{9}=1$
• B. $\frac{(x+2{)}^2}{4}+\frac{(y-3{)}^2}{9}=1$
• C. $\frac{(x-2{)}^2}{4}+\frac{(y+3{)}^2}{9}=1$
• D. $\frac{(x-2{)}^2}{9}+\frac{(y+3{)}^2}{4}=1$
• E. $\frac{(x+2{)}^2}{9}+\frac{(y+3{)}^2}{4}=1$

Answer 1

The correct option is B $\frac{(x+2{)}^2}{4}+\frac{(y-3{)}^2}{9}=1$

$\frac{{(x+2)}^2}{4}+\frac{{(y-3)}^2}{9}=1$

$2b=4,b=2$

$2a=6,a=3$

Let $ax+by+c=0$ be the major axis

Let $bx+ay+c=0$ be the minor axis

$A,B$ be lengths of major and minor axis

Equation of ellipse: $\frac{{\left(\frac{ax+by+c}{\sqrt{a^2+b^2}}\right)}^2}{{\left(\frac{A}{2}\right)}^2}+\frac{{\left(\frac{bx-ay+c}{\sqrt{a^2+b^2}}\right)}^2}{{\left(\frac{B}{2}\right)}^2}=1$