Answer
a) $\dfrac{x^2}{2500}+\dfrac{y^2}{900}=1$
b) (-40,0)$
(40,0)$
Work Step by Step
a) Determine $a,b$:
$b=30$
$2a=100\Rightarrow a=50$
Determine the equation of the ellipse:
$\dfrac{x^2}{50^2}+\dfrac{y^2}{30^2}=1$
$\dfrac{x^2}{2500}+\dfrac{y^2}{900}=1$
b) Determine the foci:
$c^2=a^2-b^2$
$c^2=50^2-30^2$
$c^2=2500-900$
$c^2=1600$
$c=\pm\sqrt {1600}=\pm 40$
The foci are:
$F_1(-c,0)=(-40,0)$
$F_2(c,0)=(40,0)$
