Name: Finding the Angle Between Two Lines
Uploaded: 2019-07-19
Duration: 9 min 3 s
Description: In this video, learn the angle between pair of lines and the nature of lines along with examples on them, which help you solve the questions in exams. Peruse and learn.

Question

The adjacent sides of a parallelogram are

2 x^{2} - 5 x y + 3 y^{2} = 0

and one diagonal is

x + y + 2 = 0

. Find the vertices and the other diagonal.

Accepted Answer

Let, $O A C B$ be the given parallelogram.

Let combined equation of $O A$ and $O B$ be $2 x^{2} - 5 x y + 3 y^{2} = 0$

$\Rightarrow 2 x^{2} - 2 x y - 3 x y + 3 y^{2} = 0$

$\Rightarrow (x - y) (2 x - 3 y) = 0$

Let $x - y = 0$ ...(i) and $2 x - 3 y = 0$ ...(ii)

The point of intersection of (i) and (ii) is $O (0, 0)$

Equation of diagonal $A B$ is $x + y + 2 = 0$ ...(iii) $(∵$ it is not passing through $O)$

Solving (i) and (iii), we get vertex $A = (- 1, - 1)$

Solving (ii) and (iii), we get vertex $B = (- \frac{6}{5}, - \frac{4}{5})$

We know that intersection point of diagonals is the midpoint of edges of diagonals.

$\Rightarrow$ Intersection point of diagonals is $\frac{O + C}{2} = \frac{A + B}{2}$ .

$4^{t h}$ vertex $C = A + B - O$

$= (- 1 - \frac{6}{5}, - 1 - \frac{4}{5})$

$= (- \frac{11}{5}, - \frac{9}{5})$

Diagonal $O C$ is the line passing through $C & O$ .

Equation of the line passing through points $(x_{1}, y_{1})$ and $(x_{2}, y_{2})$ is given by $(y - y_{1}) (x_{1} - x_{2}) = (x - x_{1}) (y_{1} - y_{2})$ .

The equation of diagonal $O C$ is $(y - 0) = \frac{\frac{- 9}{5}}{\frac{- 11}{5}} (x - 0)$

$\Rightarrow 11 y = 9 x$

The adjacent sides of a parallelogram are $2 x^{2} - 5 x y + 3 y^{2} = 0$ and one diagonal is $x + y + 2 = 0$ . Find the vertices and the other diagonal.

Important Questions on Pair of Straight Lines

Learn and Prepare for any exam you want !

The adjacent sides of a parallelogram are 2x2-5xy+3y2=0 and one diagonal is x+y+2=0. Find the vertices and the other diagonal.

Important Questions on Pair of Straight Lines

Learn and Prepare for any exam you want !

The adjacent sides of a parallelogram are $2 x^{2} - 5 x y + 3 y^{2} = 0$ and one diagonal is $x + y + 2 = 0$ . Find the vertices and the other diagonal.