# Math Help - Find equation of ellipse

1. ## Find equation of ellipse

center at (2,4), focus at (7,4), contains point (5,8)

2. ## Re: Find equation of ellipse

Originally Posted by sluggerbroth
center at (2,4), focus at (7,4), contains point (5,8)
$\frac{(x-2)^2}{a^2} + \frac{(y-4)^2}{b^2} = 1$

$c = 5$

since the focal length is in the y-direction ...

$b^2 = a^2 + c^2$

substitute the given coordinates for $x$ and $y$ and solve for $a^2$ and $b^2$

3. ## Re: Find equation of ellipse

algebra gets really, really messy??? or am i doing something wrong?????

4. ## Re: Find equation of ellipse

Originally Posted by sluggerbroth
algebra gets really, really messy??? or am i doing something wrong?????
I don't know ... you haven't shown any work.

5. ## Re: Find equation of ellipse

check that ... focus is in the x-direction (excuse my numerical dyslexia)

should be $a^2 = b^2 + c^2$