(x-2)^2 / 49 + (y+1)^2 / 25 = 1

Question

a.) what are the vertices?

b.) What are the major and minor axises?

I always have troubling understanding how to find these. :(

Any help is greatly appreciated!

Answer 1

for x^2/a^2 + y^2/b^2 = 1,

semi-major axes are a and b. Select the larger for major, smaller for minor.

so, here major=14, minor=10

foci are on the major axis, at distance c from center, where a^2 = b^2 + c^2

so, c = √(49-25) = √24 = 2√6

Knowing the distances, and the center, and the direction of the major axis, you can easily write the coordinates of the foci and vertices.

Answer 2

Thank you, @Steve !

Would you happen to know how to find the Foci for this equation?!?!

:)