Class 11

Math

Co-ordinate Geometry

Conic Sections

Find the coordinates of the foci, the vertices, the lengths of major and minor axes and the eccentricity of the ellipse $9x_{2}+4y_{2}=36$.

$9x_{2}+4y_{2}=36$

We will convert this equation into standard form.

$⇒369 x_{2}+364 y_{2}=1$

$⇒4x_{2} +9y_{2} =1$

So, this is our standard equation of ellipse with,

$a=2,b=3$

$c=b_{2}−a_{2} =9−4 =5 $

Here, as $b>a$, major-axis will be $Y−$axis.

Now, foci will be $(0,±c)=(0,±5 ).$

Vertices will be $(0,±b)=(0,±3).$

Length of major-axis $=2b=6$

Length of minor axis $=2a=4$

Eccentricity $=bc =35 .$