Find the vertices, foci, and center of the given ellipse.

Question

14y^2 + 12x^2 − 72x − 112y + 248 = 0.?

Answer 1

The equation is

To change the expressions (x ²- 6x ) and (y ² - 8y ) into a perfect square trinomial,

add (half the x coefficient)² and add (half the y coefficient)²to each side of the equation.

Compare it to standard form of  horizontal ellipse is

Where

Center (h, k )

Vertices are (h + a , k ), (h - a , k )

Foci(h + c, k ),(h - c, k )

In this case