Question

Let A (2,3) and B (-4,5) are two fixed points. A point P moves is such a way that triangle PAB =12 sq.unit, then its locus is

Answer 1

Given points are

A (2,3) and B (-4,5)

Let P(h,k) be the moving point

As per given data,

Area of ΔPAB = 12 square units

$\frac{1}{2}[x_1(y_2-y_3)+x_2(y_3-y_1)+x_3(y_1-y_2)=12$

$\frac{1}{2}[h(3-5)+2(5-k)-4(k-3)=12$

$h(-2)+2(5-k)-4(k-3)=24$

$-2h+10-2k-4k+12=24$

$-2h+10-6k+12=24$

$-2h-6k-24=0$

$h+3k+12=0$

$\therefore\;$The locus of P is

$\boxed{\bf\,x+3y+12=0}$

Find more:

A=(-2,1) B=(4,5) and c is a point on locus eqution in y square 4x find the equation of the locus of the centroid of ∆ABC

https://brainly.in/question/8903837