Question

Centre at $(0,0)$, major axis on the $y-axis$ and passes through the points $(3,2)$ and $(1,6)$.Find the values of a,b.

Answer 1

REF.Image.

Q. If $\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$ and passes though (1,6);(3,2) find a,b

$\therefore \frac{1}{a^2}+\frac{36}{b^2}=1\to \left(1\right)$

$\frac{9}{a^2}+\frac{4}{b^2}=1\to \left(2\right)$

solving (1) and (2)

$9\ast \left(1\right)-\left(2\right)$

$\Rightarrow \frac{320}{b^2}=8$

$b^2=40$

$b=2\sqrt{10}$

$\Rightarrow \frac{9}{a^2}+\frac{4}{4\times 10}=1$

$\frac{9}{a^2}=\frac{9}{10}$

$a=\sqrt{10}$