Extra Credit Prove xh2a2 yk2b2 1 Given center hk Foci h p

Extra Credit Prove : (x-h)^2/a^2 + (y-k)^2/b^2 = 1 Given: center (h,k) Foci (h plusminusc, k Vertices (hplusminusa, k)

Solution

Solution :

We know that the equation of an ellipse is

(x-h)^2/a^2+(y-k)^2/b^2=1.

Centre the point (h, k).

Then coordinate of center become (x-h, y-k)=(0,0)

Or. x =h and y=k.

And foci (+-a, 0) =(x-h, y-k)

Or. x=+-a+h, y = k

Thus foci are (+-a+h, k).