Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the equation of the ellipse, whose length of the major axis is 20 and foci are $(0,±5)$.

$a_{2}x_{2} +b_{2}y_{2} =1$

Here, Foci of ellipse $=(0±5)$

This mean, the major axis is Y-axis and $c=5$.

Length of major axis $=20$

$⇒2b=20⇒b=10$

$∴a_{2}=b_{2}−c_{2}=100−25=75$

So, the equation of the ellipse will be,