Question

Find the equation in standard form of the ellipse with center at (4,2),foci (1,2) and (7,2) and minor axis of length 10.

a.) (x-4)^2/34+(y-2)^2/25=1
b.)(x-4)^2/25+(y-2)^2/34=1
c.)(x+4)^2/34+(y+2)^2/25=1
d.)(x+4)^2/25+(y+2)^2/34=1

Answer 1

we can do this, but before we start, note that only A and B are possibilities because it has to look like
\[\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1\] where \((h,k)\) is \((4,2)\)

Answer 2

do you know what this looks like? we need that

Answer 3

actually we don't have to do any more work now
the orientation tells you that the larger number goes underneath the \(x\) term, so it is the first one