Q. 85.0( 2 Votes )

# Find the locus of

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 =

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

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) and name the moving point be C.

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

From Pythagoras theorem we have:

BC^{2} + AC^{2} = AB^{2}

From distance formula:

BC =

AC =

And AB = 4

∴

⇒

⇒

⇒

⇒

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

Thus, locus of point is

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