A line segment AM = a moves in the XOY plane | vedclass

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

Question

(B) Let the coordinates of point $A$ be $(a \cos 	heta, a \sin 	heta)$.Since $AM$ is parallel to the $X$-axis and has length $a$,the coordinates of

Vedclass · Accepted Answer

$x^2 + y^2 = 2ax$

Vedclass · Answer

(B) Let the coordinates of point $A$ be $(a \cos 	heta, a \sin 	heta)$.Since $AM$ is parallel to the $X$-axis and has length $a$,the coordinates of point $M(x, y)$ are given by $(a \cos 	heta + a, a \sin 	heta)$ or $(a \cos 	heta - a, a \sin 	heta)$.Case $1$: $x = a \cos 	heta + a$ and $y = a \sin 	heta$.Then $x - a = a \cos 	heta$ and $y = a \sin 	heta$.Squaring and adding,we get $(x - a)^2 + y^2 = a^2 \cos^2 	heta + a^2 \sin^2 	heta = a^2$.$x^2 - 2ax + a^2 + y^2 = a^2 \implies x^2 + y^2 = 2ax$.Case $2$: $x = a \cos 	heta - a$ and $y = a \sin 	heta$.Then $x + a = a \cos 	heta$ and $y = a \sin 	heta$.Squaring and adding,we get $(x + a)^2 + y^2 = a^2 \cos^2 	heta + a^2 \sin^2 	heta = a^2$.$x^2 + 2ax + a^2 + y^2 = a^2 \implies x^2 + y^2 = -2ax$.Combining these,the locus is $x^2 + y^2 = \pm 2ax$. Among the given options,$x^2 + y^2 = 2ax$ is the correct one.

$A$ line segment $AM = a$ moves in the $XOY$ plane such that $AM$ is parallel to the $X$-axis. If $A$ moves along the circle $x^2 + y^2 = a^2$,then the locus of $M$ is

Similar Questions

The locus of a point which divides the join of $A(-1, 1)$ and a variable point $B$ on the circle ${x^2} + {y^2} = 4$ in the ratio $3 : 2$ is:

If $A=(1,2)$,$B=(2,1)$ and $P$ is any point satisfying the condition $PA+PB=3$,then the equation of the locus of $P$ is

Let $A$ be the point $(1, 2)$ and $B$ be any point on the curve $x^2 + y^2 = 16$. If the centre of the locus of the point $P$,which divides the line segment $AB$ in the ratio $3:2$ is the point $C(\alpha, \beta)$,then the length of the line segment $AC$ is

$A$ circle cuts a chord of length $4a$ on the $x$-axis and passes through a point on the $y$-axis,distant $2b$ from the origin. Then the locus of the center of this circle is

The locus of the points from which perpendicular tangents can be drawn to the circle $x^2 + y^2 = a^2$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module