Locus of a point $P$ which such that $P A = P B$ where $A = (0, 3, 2)$ and $B = (2, 4, 1)$ is

2 x + y - z = 4

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

x - 2 y + z + 1 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

9 x - 2 y + 4 z - 5 = 0

No worries! We‘ve got your back. Try BYJU‘S free classes today!

None of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 x + y - z = 4$
Let the co-ordinate of $P$ be $(x, y, z)$ .
Given the points $A (0, 3.2)$ and $B (2, 4, 1)$ .
Given,
$P A = P B$ .
or, $\sqrt{x^{2} + (y - 3)^{2} + (z - 2)^{2}} = \sqrt{(x - 2)^{2} + (y - 4)^{2} + (z - 1)^{2}}$
or, $- 6 y + 9 - 4 z + 4 = - 4 x + 4 - 8 y + 16 - 2 z + 1$ [ Squaring and then eliminating the higher power of $x, y, z$ ]
or, $4 x + 2 y - 2 z = 8$
or, $2 x + y - z = 4$ .
So locus of $P$ is $2 x + y - z = 4$ .

Suggest Corrections

Similar questions

Q. A line drawn through the point P (-1, 2) meets the hyperbola

x y = c^{2}

at the points A and B (points A and B lie on same side of P) . Q is a point on AB such that PA, PQ and PB are in H.P then locus of Q is

A line drawn through the point $P (- 1, 2)$ meets the hyperbola $x y = c^{2}$ at the points $A$ and $B$ . (points $A$ and $B$ lie on same side of $P$ ) and $Q$ is a point on $A B$ such that $P A, P Q$ and $P B$ are in $H . P$ then locus of $Q$ is

A. $x - 2 y = 2 c^{2}$

B. $2 x - y = 2 c^{2}$

C. $x + 2 y = 2 c^{2}$

D. $2 x - y + 2 c^{2} = 0$

Q. The locus of a point which is equidistant from the points P(0,2,3) and Q(2,-2,1) will be .

Q. The locus of a point, such that the sum of the squares of its distance from the planes

x + y + z = 0, x - z = 0

and

x - 2 y + z = 0

9

, is

Q. A point moves such that the sum of square of it's distances from the planes

x - z = 0, x - 2 y + z = 0

and

x + y + z = 0

36.

Then the locus of the point is

Join BYJU'S Learning Program

Locus of a point P which such that PA=PB where A=(0,3,2) and B=(2,4,1) is

Locus of a point $P$ which such that $P A = P B$ where $A = (0, 3, 2)$ and $B = (2, 4, 1)$ is