(D) Let $S = (x, y)$. The given relation is $SQ^2 + SR^2 = 2SP^2$.Using the distance formula,we have:$((x + 1)^2 + y^2) + ((x - 2)^2 + y^2) = 2((x - 1

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

$A$ straight line parallel to the $y$-axis

(D) Let $S = (x, y)$. The given relation is $SQ^2 + SR^2 = 2SP^2$.Using the distance formula,we have:$((x + 1)^2 + y^2) + ((x - 2)^2 + y^2) = 2((x - 1)^2 + y^2)$Expanding the terms:$(x^2 + 2x + 1 + y^2) + (x^2 - 4x + 4 + y^2) = 2(x^2 - 2x + 1 + y^2)$$2x^2 - 2x + 5 + 2y^2 = 2x^2 - 4x + 2 + 2y^2$Subtracting $2x^2 + 2y^2$ from both sides:$-2x + 5 = -4x + 2$$2x = -3$$x = -\frac{3}{2}$This represents a straight line parallel to the $y$-axis.

Class 11 Mathematics 10-1.Circle and System of Circles Locus Related Problem

Medium

If $P(1, 0)$,$Q(-1, 0)$,and $R(2, 0)$ are three given points,then find the locus of $S(x, y)$ which satisfies the relation $SQ^2 + SR^2 = 2SP^2$.

A
$A$ straight line parallel to the $x$-axis
B
$A$ circle passing through the origin
C
$A$ circle with the origin as the center
D
$A$ straight line parallel to the $y$-axis

Explore More

Browse All

Question Bank

All Subjects

Class 11 Questions

Class 11

Mathematics Questions

Chapter

10-1.Circle and System of Circles

Subtopic

Locus Related Problem

If a circle of a constant radius $6$ passes through the origin $O$ and meets the coordinate axes at $A$ and $B$, then find the locus of the centroid of $\triangle OAB$.

MediumAP EAMCET 2021

View Solution

If a circle passes through the point $(1, 2)$ and intersects the circle $x^2 + y^2 = 4$ orthogonally,then the equation of the locus of its center is:

Difficult

View Solution

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

MediumTS EAMCET 2014

View Solution

The centroid of a variable triangle $ABC$ is at a distance of $5$ units from the origin. If $A = (2, 3)$ and $B = (3, 2)$,then the locus of $C$ is

MediumTS EAMCET 2024

View Solution

If a circle passes through the point $(a, b)$ and cuts the circle $x^2 + y^2 = K^2$ orthogonally,then the equation of the locus of its centre is:

View Solution

Vedclass Products

For Students

Vedclass Test Series

Mock tests in real JEE/NEET style with performance analysis. 5-day free trial.

Start Free Trial

For Teachers

Exam Paper Generator

Generate Set A/B/C/D exam papers from 7.5L+ questions in 2 minutes. 3 chapters free.

Try Free

For Institutes

Online Exam Module

Live online exams with unlimited students, 360° analytics & white-label branding.

See Demo

If $P(1, 0)$,$Q(-1, 0)$,and $R(2, 0)$ are three given points,then find the locus of $S(x, y)$ which satisfies the relation $SQ^2 + SR^2 = 2SP^2$.

Similar Questions

If a circle of a constant radius $6$ passes through the origin $O$ and meets the coordinate axes at $A$ and $B$, then find the locus of the centroid of $\triangle OAB$.

If a circle passes through the point $(1, 2)$ and intersects the circle $x^2 + y^2 = 4$ orthogonally,then the equation of the locus of its center is:

The locus of the centroid of the triangle with vertices at $(a \cos \theta, a \sin \theta)$,$(b \sin \theta, -b \cos \theta)$ and $(1, 0)$ is (where $\theta$ is a parameter).

The centroid of a variable triangle $ABC$ is at a distance of $5$ units from the origin. If $A = (2, 3)$ and $B = (3, 2)$,then the locus of $C$ is

If a circle passes through the point $(a, b)$ and cuts the circle $x^2 + y^2 = K^2$ orthogonally,then the equation of the locus of its centre is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module