Let A(5, -3),B(3, -2),and C(-1, 5) be three p | vedclass

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

Question

(D) Let the coordinates of point $P$ be $(x, y)$.Given the condition $PA^2 + 2PB^2 = 3PC^2$.Substituting the coordinates of $A(5, -3)$,$B(3, -2)$,and

Vedclass · Accepted Answer

$\left(2, \frac{37}{22}\right)$

Vedclass · Answer

(D) Let the coordinates of point $P$ be $(x, y)$.Given the condition $PA^2 + 2PB^2 = 3PC^2$.Substituting the coordinates of $A(5, -3)$,$B(3, -2)$,and $C(-1, 5)$:$(x - 5)^2 + (y + 3)^2 + 2[(x - 3)^2 + (y + 2)^2] = 3[(x + 1)^2 + (y - 5)^2]$Expanding the terms:$(x^2 - 10x + 25 + y^2 + 6y + 9) + 2(x^2 - 6x + 9 + y^2 + 4y + 4) = 3(x^2 + 2x + 1 + y^2 - 10y + 25)$$(x^2 + y^2 - 10x + 6y + 34) + 2(x^2 + y^2 - 6x + 4y + 13) = 3(x^2 + y^2 + 2x - 10y + 26)$$3x^2 + 3y^2 - 22x + 14y + 60 = 3x^2 + 3y^2 + 6x - 30y + 78$$-22x - 6x + 14y + 30y + 60 - 78 = 0$$-28x + 44y - 18 = 0$Dividing by $-2$:$14x - 22y + 9 = 0$Checking option $D$ $\left(2, \frac{37}{22}\right)$:$14(2) - 22\left(\frac{37}{22}\right) + 9 = 28 - 37 + 9 = 0$.Thus,the point $\left(2, \frac{37}{22}\right)$ lies on the locus.

Let $A(5, -3)$,$B(3, -2)$,and $C(-1, 5)$ be three points. If $P$ is a point satisfying the condition $PA^2 + 2PB^2 = 3PC^2$,then a point that lies on the locus of $P$ is

Similar Questions

$A$ straight line meets the $X$ and $Y$ axes at the points $A$ and $B$ respectively. If $AB = 6$ units,then the locus of the point $P$ which divides the line segment $AB$ such that $AP : PB = 2 : 1$ is

Let $P(2, -3)$ and $Q(-2, 1)$ be the vertices of the $\Delta PQR$. If the centroid of $\Delta PQR$ lies on the line $2x + 3y = 1$, then the locus of $R$ is

$ABC$ is an isosceles triangle. If the coordinates of the base are $B(1, 3)$ and $C(-2, 7)$,the coordinates of vertex $A$ can be

$A$ straight line passing through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q$. If $O$ is the origin and the rectangle $OPRQ$ is completed,then the locus of $R$ is:

$A (a, 0)$ and $B (-a, 0)$ are two fixed points of $\Delta ABC$. If the vertex $C$ moves such that $\cot A + \cot B = \lambda$,where $\lambda$ is a constant,then what is the locus of point $C$?

Vedclass Test Series

Exam Paper Generator

Online Exam Module