Question

The point on y-axis which is equidistant from (6,-1) and (2,-3) is

Answer 1

The point is on the y axis, therefore the point must be (0,y). Now, we just have to calculate the distance of this from these 2 points and equate them.

Distance of (0,y) from (6, -1):
√{(6-0)²+(-1-y)²}

Distance of (0,y) from (2, -3):
√{(2-0)²+(-3-y) ²}

Now equate both the distance:

√{(6-0)²+(-1-y)²} = √{(2-0)²+(-3-y) ²}

√{(6)²+(1+y)²} = √{(2)²+(3+y) ²}

Now square both sides,
(6)²+(1+y)²= (2)²+(3+y) ²
36+ 1+y²+ 2y= 4 + 9 + y² +6y
36+ 1= 4 + 9 +4y
37= 13 +4y
37-13= 4y
24= 4y
y = 6

Hence, the point is (0,6).

Hope you understand. All the best!