Straight Line And Pair Of Straight Lines Ques 66

Answer:

66.$7x-4y+25=0,4x+7y=11=0,7x-3=0$

Solution:

Formula:

Equation Of Lines Parallel And Perpendicular To A Given Line :

66. Let the coordinates of third vertex be $C(a, b)$.

Since, $C H$ is $\perp A B$,

$$ \begin{aligned} & \therefore \quad \frac{b}{a} = \frac{4}{-7} = -1 \\ & \Rightarrow \quad 4 b=7 a \end{aligned} $$

Also, $A H \perp B C$

$$ \begin{alignedat} & \therefore \quad-\frac{1}{5} \quad \frac{3-b}{-2-a}=-1 \\ & \Rightarrow \quad 3-b=-10-5 a \end{aligned} $$

On solving Eqs. (i) and (ii), we get

$$ a=-4, b=-7 $$