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 =

• Pythagoras theorem: In right triangle ΔABC : the sum of the square of two sides is equal to the square of its hypotenuse.

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) and name the moving point to be C.

According to a question on drawing the figure, we get a right triangle Δ ABC.

From Pythagoras theorem we have:

BC² + AC² = AB²

From distance formula:

BC =

AC =

And AB = 4

∴

⇒

⇒

⇒ 2h² + 2k² – 8 = 0

⇒ h² + k² = 4

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

Thus, the locus of a point is x² + y² = 4 ….ans