Question

Find the coordinates of the point which
is on y-axis and which is
equidistant from points C5,-2)
and (3,4).
​

Answer 1

Answer:

Let the required point P(0,y) then

AP

2

=BP

2

=(−4−0)

2

+(3−y)

2

=(5−0)

2

+(2−y)

2

⇒(−4)

2

+(3−y)

2

=(5)

2

+(2−y)

2

⇒16+9−6y+y

2

=25+4+y

2

−4y⇒2y⇒=−4⇒y=−2

Hence the required points is P(0,−2)

Answer 2

Answer:

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

Let A(5,−2) and B(−3,2). Then,

PA=PB

PA

2

=PB

2

(5−0)

2

+(−2−y)

2

=(−3−0)

2

+(2−y)

2

25+4+y

2

+4y=9+4+y

2

−4y

8y=−16

y=−2

Therefore, the required point is (0,−2).

I hope it will help you

Pls follow, thank and vote me pls pls pls