Through a point `A` on the x-axis, a straight line is drawn parallel to the y-axis so as to meet the pair of straight lines `a x^2+2h x y+b y^2=0` at `B` and `Cdot` If `A B=B C ,` then (a) `h^2=4a b` (b) `8h^2=9a b` (c) `9h^2=8a b` (d) `4h^2=a b`

Options

A. `h^(2)=4ab`
B. `8h^(2)=9ab`
C. `9h^(2)=8ab`
D. `4h^(2)=ab`

Answer

2

Explanation

Given AB=BC. Also , `m_(1)+m_(2)=(2h)/(b)andm_(1)m_(2)=(a)/(b)`
`tantheta=(AB)/(OA)=m_(1)`
and `m_(2)=tanalpha=(2AB)/(OA)=2m_(1)`
`:.(m_(2))/(m_(1))=2`
or `(m_(2)+m_(1))/(m_(2)-m_(1))=(2+1)/(2-1)=3`
or `(2h//b)/(sqrt((4h^(2)//b^(2))-(4a//b)))=3`
or `(4h^(2))/(b^(2))*(b^(2))/(4(h^(2)-ab))=9`
or `9h^(2)-9ab=h^(2)`
or `8h^(2)=9ab`