First slide

Pair of straight lines

Question

The orthocentric of the triangle formed by the lines $xy + 3 x + 3 y + 9 = 0$ and the line $3 x + 4 y - 5 = 0$ is

Moderate

A

$(3, 3)$
B

$(- 3, 3)$
C

$(3, - 3)$
D

$(- 3, - 3)$

Solution

The given pair of lines is $xy + 3 x + 3 y + 9 = 0$
The above equation represents $x + 3 = 0$ and $y + 3 = 0$ which are perpendicular
The triangle formed by the given lines is right angle triangle.
So that the ortho center of the triangle is vertex at right angle.
Hence the point of intersection of $x + 3 = 0$ and $y + 3 = 0$ is ortho center
Therefore, the ortho center is $(- 3, - 3)$

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