Question

Find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Foci: (±7, 0); major axis of length 18

Answer 1

Answer:
`(x^2)/(81)+(y^2)/(32)=1`

Explanation:

The standard form of equation of ellipse with foci (±c,0) as:

`(x^2)/(a^2)+(y^2)/(b^2)=1`

, where major axis = 2a and minor axis = 2b

Given: Foci: (±7, 0); major axis of length 18

i.e. c= 7 and 2a =18 ⇒a= 9

Also,

`c^2=a^2-b^2\Rightarrow\ b^2= a^2-c^2\\\\\Rightarrow\ b^2={9^2-7^2}={81-49}\\\\\Rightarrow\ b^2=32`

Put value of
`a^2` and
`b^2` , we get the required equation :

`(x^2)/(81)+(y^2)/(32)=1`