Find a point on the y-axis which is equidistant from A(-4, 3) and B(5,

1.	Find a point on the y-axis which is equidistant from A(-4, 3) and B(5, 2).
Answer» Let the point on the y-axis be P(0, y) Given: P is equidistant from A(- 4, 3) and B(5, 2). i.e., PA = PB ⇒ \(\sqrt{(-4-0)^2+(3-y)^2}\) = \(\sqrt{(5-0)^2+(2-y)^2}\) Squaring both sides, we get ⇒ (- 4 – 0)² + (3 – y)² = (5 – 0)² + (2 – y)² ⇒ 16 + 9 – 6y + y² = 25 + 4 – 4y + y² ⇒ 25 – 6y = 29 – 4y ⇒ 2y = - 4 ⇒ y = - 2 Therefore, the required point on the y-axis is (0, - 2).

Find a point on the y-axis which is equidistant from A(-4, 3) and B(5, 2).

Answer»

Let the point on the y-axis be P(0, y)

Given: P is equidistant from A(- 4, 3) and B(5, 2).

i.e., PA = PB

⇒ \(\sqrt{(-4-0)^2+(3-y)^2}\) = \(\sqrt{(5-0)^2+(2-y)^2}\)

Squaring both sides, we get

⇒ (- 4 – 0)² + (3 – y)² = (5 – 0)² + (2 – y)²

⇒ 16 + 9 – 6y + y² = 25 + 4 – 4y + y²

⇒ 25 – 6y = 29 – 4y

⇒ 2y = - 4

⇒ y = - 2

Therefore, the required point on the y-axis is (0, - 2).