Question

If a, b and c are real such that a² + 9b² - 4c² - 6ab = 0, then the line ax + by + c = 0 always passes through the point with negative ordinate

(A)  (-1/2, -3/2)

(B)  (1/2, 3/2)

(C)  (1/2, - 3/2)

(D)  (-1/2, 3/2)

Answer 1

Correct option  (C)  (1/2, - 3/2)

Explanation :

We have

 Therefore, the line ax + by + c = 0 passes through the points

(1/2, -3/2) and (-1/2,3/2)

 , Since the ordinate is negative, the point

(1/2, -3/2)