sir/mam, please solve the following question

Dear student,

 

The given points are A(-5, 4) and B(-1, 6).

Let the given point be P(x, y).

P is equidistant from A and B, so PA = PB or PA² = PB²

Using distance formula, we have:

(x+5)² + (y-4)² = (x+1)² + (y-6)²

x² + 25 + 10x + y² + 16 - 8y = x² + 1 + 2x + y² + 36 - 12y

8x + 4y + 4 = 0

2x + y + 1 = 0

This is the condition for the point P to be equidistant from A and B.

This is a linear equation in the variables x and y. So, there will be infinitely many points (x, y) satisfying this equation.

Thus, there will be infinitely many points which will be equidistant from A and B.

 

We hope that clarifies your query.

 

Regards,

Team

TopperLearning