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The equation of two straight lines throu...

The equation of two straight lines through the point `(x_(1),y_(1))` and perpendicular to the lines given by `ax^(2)+2hxy+by^(2)=0`, is

A

`b(x-x_1)^2-2h(x-x_1)(y-y_1)+a(y-y_1)^2=0`

B

`b(x-x_1)^2+2h(x-x_1)(y-y_1)+a(y-y_1)^2=0`

C

`a(x-x_1)^2-2h(x-x_1)(y-y_1)+b(y-y_1)^2=0`

D

None of these

Text Solution

Verified by Experts

The correct Answer is:
A
We know that the equations of the lines passing through the origin and perpendicular to the lines given by `ax^2+2hxy+by^2=0`is `bx^2-2hxy+ay^2=0`
Now , shifting the origin at `(x_1,y_1)`, the equations of the required lines are `b(x-x_1)^2-2h(x-x_1)(y-y_1)+a(y-y_1)^2=0`
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