Let the equations of | Straight Lines

JEE MAIN 2019

09-01-19 S2

Question

Let the equations of two sides of a triangle be $3 x-2 y+6=0$ and $4 x+5 y-20=0$. If the orthocentre of this triangle is at (1 1) then the equation of its third side is

Select the correct option:

$26 x-122 y-1675=0$

$122 y-26 x-1675=0$

$122 y+26 x+1675=0$

$26 x+61 y+1675=0$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution

$\begin{aligned} & \left(x_1, \frac{3 x_1+6}{2}\right) \\ & \therefore m_{A H-}-m_{B C}=1 \\ & \frac{15-4 x_2}{5\left(x_2-1\right)}=-\frac{2}{3} \\ & 45-12 x_2=-10 x_2+10 \\ & 2 x_2=35 \Rightarrow x_2=\frac{3 x_2}{2}-1 \\ & 2\end{aligned}$

Question Tags

JEE Main

Mathematics

Hard

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