Answer:
h = 1, k = 2, a = 6 and b = 2.
Explanation:
Start by grouping the terms in x and y together:
4x^2 - 8x + 36y^2 - 144y = -4
Factor out the coefficient:
4(x^2 - 2x) + 36(y^2 - 4y) = -4
Complete the squares:
4 [(x - 1)^2 - 1] + 36 [y - 2)2 - 4] = -4
4(x - 1)^2 - 4 + 36(y - 2)^2 - 144 = -4
4(x - 1)^2 + 36(y - 2)^2 = 144
Divide through by 144:
(x - 1)^2 / 36 + (y - 2)^2/ 4 = 1
(x - 1)^2 / 6^2 + (y - 2)^2 / 2^2 = 1 (answer).