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Let,y = x line is median of the triangle...

Let,`y = x` line is median of the triangle OAB where O is origin. Equation `ax^(2) +2hxy +by^(2) = 0,a,h,b in 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

Text Solution

Verified by Experts

The correct Answer is:
C
Since (3,3) is the mid-point of AB.
`:.` We can suppose that the coordinates of A are `(3,3+alpha)` and coordinates of B are `(3,3-alpha)`
Slope of `OA = 2xx` (slope of OB)
`:. (3+alpha)/(3) = 2 (3-alpha)/(3) rArr alpha =1`
`:.` Combined equation of OA and OB is
`(2x-3y) (4x-3y) =0`
i.e. `8x^(2) -18xy +9y^(2) =0`
`:. a+2h +b = 8 -18 +9 =- 1`
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