The equation of the line,passing through the | vedclass

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

Question

(A) The given line is $x \cos 	heta - y \sin 	heta = a$. Its slope is $m' = \frac{\cos 	heta}{\sin 	heta} = \cot 	heta$. The slope of the line pe

Vedclass · Accepted Answer

$2x \sin 	heta + 2y \cos 	heta = a \sin 2	heta$

Vedclass · Answer

(A) The given line is $x \cos 	heta - y \sin 	heta = a$. Its slope is $m' = \frac{\cos 	heta}{\sin 	heta} = \cot 	heta$. The slope of the line perpendicular to it is $m = -\frac{1}{m'} = -	an 	heta$. The equation of the line passing through $(a \cos^3 	heta, a \sin^3 	heta)$ with slope $m = -	an 	heta$ is: $y - a \sin^3 	heta = -	an 	heta (x - a \cos^3 	heta)$ $y - a \sin^3 	heta = -\frac{\sin 	heta}{\cos 	heta} (x - a \cos^3 	heta)$ $y \cos 	heta - a \sin^3 	heta \cos 	heta = -x \sin 	heta + a \cos^3 	heta \sin 	heta$ $x \sin 	heta + y \cos 	heta = a \sin 	heta \cos 	heta (\sin^2 	heta + \cos^2 	heta)$ $x \sin 	heta + y \cos 	heta = a \sin 	heta \cos 	heta$ Multiplying by $2$,we get: $2x \sin 	heta + 2y \cos 	heta = a \sin 2	heta$.

The equation of the line,passing through the point $(a \cos^3 \theta, a \sin^3 \theta)$ and perpendicular to the line $x \cos \theta - y \sin \theta = a$,is

Similar Questions

The line $MN$ whose equation is $x-y-2=0$ cuts the $X$-axis at $M$ and the coordinates of $N$ are $(4,2)$. The line $MN$ is rotated about $M$ through $45^{\circ}$ in the anticlockwise direction. What is the equation of the line $MN$ in the new position?

Reduce the following equation into intercept form and find its intercepts on the axes: $4x - 3y = 6$.

Find the equation of the line passing through the point $(1, -2)$ and making equal intercepts on the axes.

If a straight line is at a distance of $10$ units from the origin and the perpendicular drawn from the origin to it makes an angle of $\frac{\pi}{4}$ with the negative $X$-axis in the negative direction,then the equation of that line is:

Find the equation of the line passing through the point $(4, 3)$ such that the sum of its intercepts on the axes is $-1$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module