Find the equation of a line which passes thro | vedclass

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

Question

(A) The given line is $x \cos 	heta - y \sin 	heta = 2 \cos 2 	heta$. Comparing this with $y = mx + c$,the slope $m_1 = \frac{\cos 	heta}{\sin 	h

Vedclass · Accepted Answer

$x \sec 	heta + y \operatorname{cosec} 	heta = 2$

Vedclass · Answer

(A) The given line is $x \cos 	heta - y \sin 	heta = 2 \cos 2 	heta$. Comparing this with $y = mx + c$,the slope $m_1 = \frac{\cos 	heta}{\sin 	heta}$. The slope of the line perpendicular to this line is $m_2 = -\frac{1}{m_1} = -\frac{\sin 	heta}{\cos 	heta}$. The equation of the line passing through $(2 \cos^3 	heta, 2 \sin^3 	heta)$ with slope $m_2$ is: $y - 2 \sin^3 	heta = -\frac{\sin 	heta}{\cos 	heta} (x - 2 \cos^3 	heta)$ $y \cos 	heta - 2 \sin^3 	heta \cos 	heta = -x \sin 	heta + 2 \cos^3 	heta \sin 	heta$ $x \sin 	heta + y \cos 	heta = 2 \sin 	heta \cos 	heta (\cos^2 	heta + \sin^2 	heta)$ Since $\cos^2 	heta + \sin^2 	heta = 1$,we have: $x \sin 	heta + y \cos 	heta = 2 \sin 	heta \cos 	heta$ Dividing both sides by $\sin 	heta \cos 	heta$: $\frac{x \sin 	heta}{\sin 	heta \cos 	heta} + \frac{y \cos 	heta}{\sin 	heta \cos 	heta} = \frac{2 \sin 	heta \cos 	heta}{\sin 	heta \cos 	heta}$ $x \sec 	heta + y \operatorname{cosec} 	heta = 2$.

Find the equation of a line which passes through $(2 \cos^3 \theta, 2 \sin^3 \theta)$ and is perpendicular to the line $x \cos \theta - y \sin \theta = 2 \cos 2 \theta$.

Similar Questions

The coordinates of the foot of the perpendicular from the point $(2, 3)$ on the line $x + y - 11 = 0$ are

The foot of the perpendicular drawn from the origin to the line $3x + 4y - 5 = 0$ is

The coordinates of the foot of the perpendicular from $(0,0)$ upon the line $x+y=2$ are

If $2x + 3y = 5$ is the perpendicular bisector of the line segment joining the points $A\left(1, \frac{1}{3}\right)$ and $B$,then $B$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module