Find an equation for the conic that satisfies the given conditions:
Ellipse, Foci $(-4,0)$ and $(4,0)$, passes through $(-4,1.8)$.
I know how to do these questions with the vertices, but I'm kinda lost figuring this one out.
analytic geometryconic sections
Find an equation for the conic that satisfies the given conditions:
Ellipse, Foci $(-4,0)$ and $(4,0)$, passes through $(-4,1.8)$.
I know how to do these questions with the vertices, but I'm kinda lost figuring this one out.
Best Answer
Let $c = \sqrt{a^2-b^2}$. We know $c = 4$; so $16=a^2-b^2$ and $b^2+16=a^2$. Now you substitute in: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$
You obtain: $$\frac{4^2}{b^2+16}+\frac{1.8^2}{b^2}=1$$
Solving for $b$, we find $b=3$ and $a=5$. The equation is: $$\frac{x^2}{25}+\frac{y^2}{9}=1$$