(D) Let the coordinates of point $S$ be $(x, y)$.Given the relation $SQ^2 + SR^2 = 2SP^2$.Substituting the coordinates,we get:$((x + 1)^2 + (y - 0)^2)

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

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

(D) Let the coordinates of point $S$ be $(x, y)$.Given the relation $SQ^2 + SR^2 = 2SP^2$.Substituting the coordinates,we get:$((x + 1)^2 + (y - 0)^2) + ((x - 2)^2 + (y - 0)^2) = 2((x - 1)^2 + (y - 0)^2)$$(x^2 + 2x + 1 + y^2) + (x^2 - 4x + 4 + y^2) = 2(x^2 - 2x + 1 + y^2)$$2x^2 - 2x + 5 + 2y^2 = 2x^2 - 4x + 2 + 2y^2$$-2x + 5 = -4x + 2$$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

Easy

If $P = (1, 0)$,$Q = (-1, 0)$,and $R = (2, 0)$ are three given points,then the locus of a point $S$ satisfying the relation $SQ^2 + SR^2 = 2SP^2$ is

IIT 1988 All IIT

A
$A$ straight line parallel to $x$-axis
B
$A$ circle through origin
C
$A$ circle with centre at the origin
D
$A$ straight line parallel to $y$-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

Previous Year

IIT 1988 Paper All IIT years →

The equation of the locus of the midpoints of the chords of the circle $4x^2 + 4y^2 - 12x + 4y + 1 = 0$ that subtend an angle of $\frac{2\pi}{3}$ at its center is

View Solution

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of the perpendicular from $O$ on $AB$ is

DifficultJEE MAIN 2019

View Solution

The equation of the director circle of the circle ${x^2} + {y^2} = {a^2}$ is

Easy

View Solution

Let $PQ$ and $MN$ be two straight lines touching the circle $x^{2}+y^{2}-4x-6y-3=0$ at the points $A$ and $B$ respectively. Let $O$ be the centre of the circle and $\angle AOB=\pi/3$. Then the locus of the point of intersection of the lines $PQ$ and $MN$ is:

DifficultJEE MAIN 2026

View Solution

The locus of the point of intersection of tangents to the circle $x = a \cos \theta, y = a \sin \theta$ at the points whose parametric angles differ by $\pi / 2$ is:

Medium

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 the locus of a point $S$ satisfying the relation $SQ^2 + SR^2 = 2SP^2$ is

Similar Questions

The equation of the locus of the midpoints of the chords of the circle $4x^2 + 4y^2 - 12x + 4y + 1 = 0$ that subtend an angle of $\frac{2\pi}{3}$ at its center is

If a circle of radius $R$ passes through the origin $O$ and intersects the coordinate axes at $A$ and $B,$ then the locus of the foot of the perpendicular from $O$ on $AB$ is

The equation of the director circle of the circle ${x^2} + {y^2} = {a^2}$ is

Let $PQ$ and $MN$ be two straight lines touching the circle $x^{2}+y^{2}-4x-6y-3=0$ at the points $A$ and $B$ respectively. Let $O$ be the centre of the circle and $\angle AOB=\pi/3$. Then the locus of the point of intersection of the lines $PQ$ and $MN$ is:

The locus of the point of intersection of tangents to the circle $x = a \cos \theta, y = a \sin \theta$ at the points whose parametric angles differ by $\pi / 2$ is:

Vedclass Test Series

Exam Paper Generator

Online Exam Module