A point moves such that the sum of the square | vedclass

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

Question

(B) Let $P(h, k)$ be any point on the locus.Given that the sum of the squares of its distances from $A(1, 2)$ and $B(-2, 1)$ is $6$.$(PA)^2 + (PB)^2 =

Vedclass · Accepted Answer

a circle with centre $(-\frac{1}{2}, \frac{3}{2})$ and radius $\frac{1}{\sqrt{2}}$

Vedclass · Answer

(B) Let $P(h, k)$ be any point on the locus.Given that the sum of the squares of its distances from $A(1, 2)$ and $B(-2, 1)$ is $6$.$(PA)^2 + (PB)^2 = 6$$(h - 1)^2 + (k - 2)^2 + (h + 2)^2 + (k - 1)^2 = 6$$(h^2 - 2h + 1) + (k^2 - 4k + 4) + (h^2 + 4h + 4) + (k^2 - 2k + 1) = 6$$2h^2 + 2k^2 + 2h - 6k + 10 = 6$$2h^2 + 2k^2 + 2h - 6k + 4 = 0$$h^2 + k^2 + h - 3k + 2 = 0$Replacing $(h, k)$ with $(x, y)$,the locus is $x^2 + y^2 + x - 3y + 2 = 0$.This is the equation of a circle.The centre is $(-\frac{1}{2}, \frac{3}{2})$ and the radius is $\sqrt{(-\frac{1}{2})^2 + (\frac{3}{2})^2 - 2} = \sqrt{\frac{1}{4} + \frac{9}{4} - 2} = \sqrt{\frac{10}{4} - 2} = \sqrt{\frac{5}{2} - 2} = \sqrt{\frac{1}{2}} = \frac{1}{\sqrt{2}}$.

$A$ point moves such that the sum of the squares of its distances from the points $(1, 2)$ and $(-2, 1)$ is always $6$. Then,its locus is

Similar Questions

The locus of a point which divides the join of $A(-1, 1)$ and a variable point $B$ on the circle ${x^2} + {y^2} = 4$ in the ratio $3 : 2$ is:

From the point $A(0, 3)$ on the circle $x^2 + 4x + (y - 3)^2 = 0$,a chord $AB$ is drawn and extended to a point $M$ such that $AM = 2 AB$. The equation of the locus of $M$ is:

The locus of the centers of the circles,which have the same area and have $3x - 4y + 4 = 0$ and $6x - 8y - 7 = 0$ as their common tangents,is

If the tangents drawn from a point $P$ to the circle $x^2 + y^2 = a^2$ are perpendicular to the tangents drawn to the circle $x^2 + y^2 = b^2$,then the locus of $P$ is:

The locus of the centre of the circles passing through the origin and cutting off a chord of length $2$ units on the line $x=1$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module