(A) The origin $O$ is $(0,0)$ and point $A$ is $(3,4)$.Since the line segment $OP$ is parallel to $OA$ and both share the common point $O$,the points

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(A) The origin $O$ is $(0,0)$ and point $A$ is $(3,4)$.Since the line segment $OP$ is parallel to $OA$ and both share the common point $O$,the points $O, A,$ and $P$ must be collinear.The slope of line $OA$ is $m = \frac{4-0}{3-0} = \frac{4}{3}$.Since $P(x,y)$ lies on the line passing through $O(0,0)$ with slope $m = \frac{4}{3}$,the equation of the locus is $y - 0 = \frac{4}{3}(x - 0)$.This simplifies to $3y = 4x$,or $4x - 3y = 0$.

Class 11 Mathematics Straight Line Locus of Point

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$O$ is the origin and $A$ is the point $(3,4)$. If a point $P(x,y)$ moves such that the line segment $OP$ is always parallel to the line segment $OA$,then the equation of the locus of $P$ is:

A
$4x - 3y = 0$
B
$4x + 3y = 0$
C
$3x + 4y = 0$
D
$3x - 4y = 0$

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Straight Line

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Locus of Point

$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is

DifficultAP EAMCET 2012

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Let $BC$ be a fixed line segment in the plane. The locus of a point $A$ such that the $\triangle ABC$ is isosceles,is (with finitely many possible exceptional points)

KVPY 2017

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The point $P(2, 1)$ is translated to a point $Q$ parallel to the line $L \equiv x-y-4=0$ by $2 \sqrt{3}$ units. If the point $Q$ lies in the third quadrant,then the equation of the line passing through $Q$ and perpendicular to $L$ is

DifficultAP EAMCET 2023

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Given $A(1, 1)$ and $AB$ is any line through it cutting the $x-$ axis in $B$. If $AC$ is perpendicular to $AB$ and meets the $y-$ axis in $C$,then the equation of the locus of the midpoint $P$ of $BC$ is

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$A$ line is at a constant distance $c$ from the origin and meets the coordinate axes in $A$ and $B$. The locus of the centre of the circle passing through $O, A, B$ is

EasyTS EAMCET 2002

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$O$ is the origin and $A$ is the point $(3,4)$. If a point $P(x,y)$ moves such that the line segment $OP$ is always parallel to the line segment $OA$,then the equation of the locus of $P$ is:

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$A$ point moves in the $xy$-plane such that the sum of its distances from two mutually perpendicular lines is always equal to $5$ units. The area (in sq units) enclosed by the locus of the point is

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