(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

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$A$ 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

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10-1.Circle and System of Circles

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Locus Related Problem

At which point on the line $x = 3$ are the tangents drawn to the circle $x^2 + y^2 = 8$ perpendicular to each other?

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Find the locus of a point from which the lengths of the tangents drawn to the two circles $x^2 + y^2 - 5x - 3 = 0$ and $3x^2 + 3y^2 + 2x + 4y - 6 = 0$ are equal.

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The sum of the squares of the distances of a moving point from two fixed points $A(a, 0)$ and $B(-a, 0)$ is equal to a constant $2c^2$. Then,the equation of its locus is:

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$A$ stick of length $10$ units rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is:

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The locus of a point,which moves such that the sum of squares of its distances from the points $(0,0), (1,0), (0,1), (1,1)$ is $18$ units,is a circle of diameter $d$. Then $d^{2}$ is equal to ...... .

MediumJEE MAIN 2021

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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

At which point on the line $x = 3$ are the tangents drawn to the circle $x^2 + y^2 = 8$ perpendicular to each other?

Find the locus of a point from which the lengths of the tangents drawn to the two circles $x^2 + y^2 - 5x - 3 = 0$ and $3x^2 + 3y^2 + 2x + 4y - 6 = 0$ are equal.

The sum of the squares of the distances of a moving point from two fixed points $A(a, 0)$ and $B(-a, 0)$ is equal to a constant $2c^2$. Then,the equation of its locus is:

$A$ stick of length $10$ units rests against the floor and a wall of a room. If the stick begins to slide on the floor,then the locus of its middle point is:

The locus of a point,which moves such that the sum of squares of its distances from the points $(0,0), (1,0), (0,1), (1,1)$ is $18$ units,is a circle of diameter $d$. Then $d^{2}$ is equal to ...... .

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