Which of the following pairs of straight line | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The condition for a pair of straight lines represented by the general equation $ax^2 + 2hxy + by^2 = 0$ to be perpendicular is that the sum of the

Vedclass · Accepted Answer

$2 x^2 = y(x + 2 y)$

Vedclass · Answer

(A) The condition for a pair of straight lines represented by the general equation $ax^2 + 2hxy + by^2 = 0$ to be perpendicular is that the sum of the coefficients of $x^2$ and $y^2$ must be zero,i.e.,$a + b = 0$.For option $A$: $2 x^2 = y(x + 2 y)$$\Rightarrow 2 x^2 - xy - 2 y^2 = 0$Here,$a = 2$ and $b = -2$.Sum of coefficients: $a + b = 2 + (-2) = 0$.Since the condition $a + b = 0$ is satisfied,the lines represented by this equation are perpendicular.

Which of the following pairs of straight lines intersect at right angles?

Similar Questions

If the slopes of both the lines given by $x^2 + 2hxy + 6y^2 = 0$ are positive and the angle between these lines is $\operatorname{Tan}^{-1}\left(\frac{1}{7}\right)$,then find the value of $h$.

If $ax^2+2hxy+by^2+2gx+2fy+c=0$ represents a pair of parallel lines,then $\sqrt{\frac{g^2-ac}{f^2-bc}}$ is equal to

The angle between the lines $xy = 0$ is equal to .............. $^\circ$.

The angle between the lines $xy = 0$ is ............. $^\circ$.

If the slope of one of the lines represented by $2x^2 + 3xy + ky^2 = 0$ is $2$,then the angle between the pair of lines is

Vedclass Test Series

Exam Paper Generator

Online Exam Module