If A (-1, 1) and B (2, 3) are two fixed points, find the locus of a point P so that the area d ΔPAB = 8 sq. units.
Key points to solve the problem:
• Idea of distance formula- Distance between two points A(x1,y1) and B(x2,y2) is given by- AB =
Area of a ΔPQR – Let P(x1,y1) , Q(x2,y2) and R(x3,y3) be the 3 vertices of ΔPQR.
Ar(ΔPQR) =
How to approach: To find the locus of a point we first assume the coordinate of the point to be (h, k) and write a mathematical equation as per the conditions mentioned in the question and finally replace (h, k) with (x, y) to get the locus of the point.
Let the coordinates of a point whose locus is to be determined to be (h, k). Name the moving point to be C
Given the area of ΔABC = 8
According to question:
8 =
⇒ 16=|-3+k+2k-2+h-3h|
⇒ |3k-2h-5|=16
∴ 3k-2h-5=16 or 3k-2h-5= -16
⇒ 3k-2h-21=0 or 3k-2h+11=0
Replace (h,k) with (x,y)
Thus, locus of point is 3y-2x-21=0 or 3y-2x+11=0 …….ans