(D) Let the point be $P(x, y)$.Given that $PA^2 + PB^2 = AB^2$.The distance $AB = \sqrt{(2 - (-2))^2 + (0 - 0)^2} = \sqrt{4^2} = 4$,so $AB^2 = 16$.The

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(D) Let the point be $P(x, y)$.Given that $PA^2 + PB^2 = AB^2$.The distance $AB = \sqrt{(2 - (-2))^2 + (0 - 0)^2} = \sqrt{4^2} = 4$,so $AB^2 = 16$.The distance $PA^2 = (x - 2)^2 + (y - 0)^2 = x^2 - 4x + 4 + y^2$.The distance $PB^2 = (x + 2)^2 + (y - 0)^2 = x^2 + 4x + 4 + y^2$.Summing these: $(x^2 - 4x + 4 + y^2) + (x^2 + 4x + 4 + y^2) = 16$.$2x^2 + 2y^2 + 8 = 16$.$2x^2 + 2y^2 = 8$.$x^2 + y^2 = 4$,which is $x^2 + y^2 - 4 = 0$.

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

Easy

$A$ point moves in such a way that the sum of the squares of its distances from the points $A(2, 0)$ and $B(-2, 0)$ is always equal to the square of the distance between $A$ and $B$. The locus of the point is

A
$x^2 + y^2 - 2 = 0$
B
$x^2 + y^2 + 2 = 0$
C
$x^2 + y^2 + 4 = 0$
D
$x^2 + y^2 - 4 = 0$

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10-1.Circle and System of Circles

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Locus Related Problem

If the coordinates of a moving point $P$ are $(\cos \theta + \sin \theta, \sin \theta - \cos \theta)$,where $\theta$ is a parameter,find the locus of $P$.

Easy

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The angle between the tangents drawn from a point $P$ to the circle $x^2 + y^2 + 4x - 2y - 4 = 0$ is $60^{\circ}$. The locus of $P$ is:

Medium

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If the lengths of the tangents drawn from $P$ to the circles $x^2+y^2-2x+4y-20=0$ and $x^2+y^2-2x-8y+1=0$ are in the ratio $2:1$,then the locus of $P$ is

EasyAP EAMCET 2018

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The locus of the mid-points of chords of the circle $x^{2}+y^{2}=1$,which subtend a right angle at the origin,is

DifficultWBJEE 2016

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Consider a rigid square $ABCD$ as in the figure with $A$ and $B$ on the $X$ and $Y$-axes,respectively. When $A$ and $B$ slide along their respective axes,the locus of $C$ forms a part of

KVPY 2017

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$A$ point moves in such a way that the sum of the squares of its distances from the points $A(2, 0)$ and $B(-2, 0)$ is always equal to the square of the distance between $A$ and $B$. The locus of the point is

Similar Questions

If the coordinates of a moving point $P$ are $(\cos \theta + \sin \theta, \sin \theta - \cos \theta)$,where $\theta$ is a parameter,find the locus of $P$.

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