Given an ellipse, transform its equation 3x^2 + 4y^2 − 24𝑥 - 16𝑦 + 16 = 0 into its standard form.

Answer 1

3x^2 + 4y^2 - 24x - 16y + 16 = 0. GIVEN

3(x^2 - 8x) + 4(y^2 - 4y) = -16. Get ready to complete the square, twice.

3(x^2 - 8x + 16) + 4(y^2 - 4y + 4) = -16 + 3*16 + 4*4

3(x - 4)^2 + 4(y- 2)^2 = 48

(3/48) * (x - 4)^2 + (4/48) * (y - 2)^2 = 1

(1/16) * (x - 4)^2 + (1/12) * (y - 2)^2 = 1

Ellipse with center at (h,k) = (4, 2)