Class 11

Math

3D Geometry

Conic Sections

Find the equation for the ellipse that satisfies the given conditions: Centre at $(0,0)$, major axis on the $y$-axis and passes through the points $(3,2)$ and $(1,6).$

$b_{2}x_{2} +a_{2}y_{2} =1...(1)$

where $a$ is the semi-major axis.

The ellipse passes through points $(3,2)$ and $(1,6)$.

Hence, $b_{2}9 +a_{2}4 =1...(2)$

$b_{2}1 +a_{2}36 =1...(3)$

On solving equations (2) and (3), we obtain $b_{2}=10$ and $a_{2}=40$

Thus the equation of the ellipse is $10x_{2} +40y_{2} =1$ or $4x_{2}+y_{2}=40$

$b_{2}1 +a_{2}36 =1...(3)$

On solving equations (2) and (3), we obtain $b_{2}=10$ and $a_{2}=40$

Thus the equation of the ellipse is $10x_{2} +40y_{2} =1$ or $4x_{2}+y_{2}=40$