Answer to Question #270952 in Analytic Geometry for Angel Nodado

Question

Use the information provided to write the standard form equation of ellipse. Then sketch

the graph.

Foci: (-10, 16), (-10,-8)

Endpoints of major axis: (-10, 17),(-10,-9)

Answer 1

Vertices: $(-10, 17),(-10,-9)$

Major axis is vertical, length $=17-(-9)=26=2a=>a=13$

$$17-13=4=-9-(-13)$$

Center: $(-10, 4)$

Foci: $(-10, 16), (-10,-8)$

$$2c=16-(-8)=24=>c=12$$

$$c^2=a^2-b^2=>b^2=13^2-12^2=25=>b=5$$

The equation of the ellipse

$$\dfrac{(y-4)^2}{169}+\dfrac{(x+10)^2}{25}=1$$