Question

Equation of the ellipse with foci $(2\pm \sqrt{7},3)$ and the lengths of major and minor axes are $8,6$ respectively is

• A. $9(x-2{)}^2+16(y-3{)}^2=144$
• B. $16(x+2{)}^2+9(y+3{)}^2=144$
• C. $9(x-2{)}^2+36(y+3{)}^2=144$
• D. $9(x+2{)}^2+36(y-3{)}^2=144$

Answer 1

The correct option is A $9(x-2{)}^2+16(y-3{)}^2=144$

Given foci are $(2\underset{–}{+}\sqrt{7},3)$
then,Center of ellipse will be $(2,3)$
and lengths of major$\left(2a\right)$ and minor$\left(2b\right)$ axis are $8,6$ respectively.
Now equation of ellipse will be $\frac{{(x-2)}^2}{a^2}+\frac{{(y-3)}^2}{b^2}=1⟹9{(x-2)}^2+16{(y-3)}^2=144$.