Question

The equation of the ellipse with its focus at (6, 2), centre at (1, 2) and which passes through the point (4, 6) is

• A.
• B.
• C.
• D.

Answer 1

The correct option is D

Given that one focus S = (6, 2), centre C = (1, 2),P = (4, 6)
The other focus S’ = (–4, 2) (since C is the midpoint of SS’)
SS’ = 2ae $\Rightarrow$ 2ae = 10 $\Rightarrow$ ae = 5;
$SP+S^{\prime }P=2a\Rightarrow 2\sqrt{5}+4\sqrt{5}\Rightarrow a=3\sqrt{5}\Rightarrow a^2=45$ and $b^2=a^2-a^2{e}^2\Rightarrow b^2=20$
$\therefore$ Equation of the ellipse is $\frac{(x-1{)}^2}{45}+\frac{(y-2{)}^2}{20}=1$