Question

Let y = x line is median of the triangle OAB where O is origin. Equation ax² + 2hxy + by² = 0, a, h, b Ī N, represents combined equation of OA and OB. A and B lie on the ordinate x = 3. If slope of OA is twice the slope of OB, then greatest possible value of a + 2h + b is-

• A. 0
• B. – 2
• C. – 1
• D. Does not exist

Answer 1

Answer: (C)

– 1

Answer 2

Since (3, 3) is the mid-point of AB.

\ we can suppose that the coordinates of A are (3, 3 + a) and coordinates of B are (3, 3 – a)

\ $\frac{3 + \alpha}{3}$ = 2 $\frac{3 - \alpha}{3}$i.e. a = 1

\ combined equation of OA and OB is

(2x – 3y) (4x – 3y) = 0

i.e. 8x² – 18xy + 9y² = 0

\ a + 2h + b = 8 – 18 + 9 = – 1