Question

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and $\sqrt{3}$ and their corresponding equations are y-5=0 and x+3=0, then write the equation of the ellipse are 2 and $\sqrt{3}$ and their corresponding equations are y-5=0 and x+3=0, then write the equation of the ellipse.

Answer 1

Evaluate of semi-major and semi-minor axes are y-5=0 and x+3=0
x=-3, y=5
Thus, centre of ellipse is (-3,5)
$a=2,b=\sqrt{3}$
Evaluate of ellipse is,
$\frac{(x-h{)}^2}{a^2}+\frac{(y-k{)}^2}{b^2}=1$
$\frac{(x+3{)}^2}{(2{)}^2}+\frac{(y-5{)}^2}{(\sqrt{3}{)}^2}=1$
$3(x+3{)}^2+4(y-5{)}^2=12$
$3x^2+27+18x+4y^2+100-40y=12$
$3x^2+4y^2+18x-40y+115=0$