Q. 9

# 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.

Answer :

Key points to solve the problem:

• Idea of distance formula- Distance between two points A(x_{1},y_{1}) and B(x_{2},y_{2}) is given by- AB =

Area of a ΔPQR – Let P(x_{1,}y_{1}) , Q(x_{2},y_{2}) and R(x_{3},y_{3}) be the 3 vertices of ΔPQR.

Ar(ΔPQR) =

How to approach: To find locus of a point we first assume the coordinate of point to be (h, k) and write a mathematical equation as per the conditions mentioned in question and finally replace (h, k) with (x, y) to get the locus of point.

Let the coordinates of point whose locus is to be determined be (h, k). Name the moving point be C

Given area of ΔABC = 8

According to question:

8 =

⇒

⇒

∴

⇒

Replace (h,k) with (x,y)

Thus, locus of point is …

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