Question

7x²+3y²-28x-12y=-19

Answer 1

Complete the square for x and y.

7x^2 + 3y^2 - 28x - 12y = -19

7x^2 - 28x + 3y^2 - 12y = -19

7(x^2 - 4x) + 3(y^2 - 4y) = -19

7(x^2 - 4x + 4) + 3(y^2 - 4y + 4) = -19 + 28 + 12

7(x - 2)^2 + 3(y - 2)^2 = 21

$\dfrac{(x - 2)^2}{3} + \dfrac{(y - 2)^2}{7} = 1$