If the lines represented by (1+sin^2 theta) x | vedclass

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

Question

(C) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.If these lines are perpendicular

Vedclass · Accepted Answer

$\frac{3\pi}{2}$

Vedclass · Answer

(C) The general equation of a pair of straight lines passing through the origin is given by $ax^2 + 2hxy + by^2 = 0$.If these lines are perpendicular to each other,the condition is $a + b = 0$.Given the equation $(1+\sin^2 	heta) x^2 + 2hxy + 2\sin 	heta y^2 = 0$,we identify $a = 1+\sin^2 	heta$ and $b = 2\sin 	heta$.Applying the condition $a + b = 0$:$(1+\sin^2 	heta) + 2\sin 	heta = 0$$(1+\sin 	heta)^2 = 0$$1+\sin 	heta = 0$$\sin 	heta = -1$For $	heta \in [0, 2\pi]$,the value of $	heta$ satisfying $\sin 	heta = -1$ is $	heta = \frac{3\pi}{2}$.

If the lines represented by $(1+\sin^2 \theta) x^2+2hxy+2\sin \theta y^2=0$,where $\theta \in [0, 2\pi]$,are perpendicular to each other,then $\theta = \dots$.

Similar Questions

If $ax^2+6xy+by^2-10x+10y-6=0$ represents a pair of perpendicular lines,then the value of $|a|$ equals

If the angle between the lines given by $x^2-3xy+\lambda y^2+3x-5y+2=0$ where $\lambda \geq 0$ is $\tan^{-1}\left(\frac{1}{3}\right)$,then the value of $\lambda$ is

If the equation $x^{2}-3xy+\lambda y^{2}+3x-5y+2=0$ represents a pair of lines,where $\lambda$ is a real number and $\theta$ is the angle between them,then the value of $\operatorname{cosec}^{2} \theta$ is

If the lines represented by the equation $(p - q)x^2 + 2(p + q)xy + (q - p)y^2 = 0$ are mutually perpendicular,then:

The measure of the angle between the lines $x^{2}+2xy \operatorname{cosec} \alpha+y^{2}=0$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module