Question

A(5, 3), B(3, -2) are two fixed points, find the equation to the locus of a point P which moves so that the area of the triangle PAB is 9 units.

Answer 1

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 = \(\sqrt{(x_2-x_1)^2+(y_2-y_1)^2}\)

Area of a ΔPQR – Let P(x₁, y₁) , Q(x₂, y₂) and R(x₃, y₃) be the 3 vertices of 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 = 9

According to question: