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: $\dfrac{x^2}{81}+\dfrac{y^2}{32}=1$

Step-by-step explanation:

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

$\dfrac{x^2}{a^2}+\dfrac{y^2}{b^2}=1$

, 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 :

$\dfrac{x^2}{81}+\dfrac{y^2}{32}=1$