Question

find a point on the y-axis equidistant from(-5,2) & (9,-2​

Answer 1

Let us consider the point on the y-axis be (0, y).

Given: (0, y) is equidistant from the points (- 5, 2) and (9, - 2).

This gives:

$\small{\mathsf{\sqrt{(0+5)^2+(y-2)^{2}}=\sqrt{(0-9)^{2}+(y+2)^{2}}}}$

$\to \small{\mathsf{\sqrt{25+y^{2}-4y+4}=\sqrt{81+y^{2}+4y+4}}}$

$\to \mathsf{\sqrt{y^{2}-4y+29}=\sqrt{y^{2}+4y+89}}$

$\to \mathsf{y^{2}-4y+29=y^{2}+4y+85}$

$\to \mathsf{8y=-56}$

$\to \mathsf{y=-7}$

∴ the required point is (0, - 7).

Answer 2

Step-by-step explanation:

I hope it is helpful for u