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If point $A (− 1, y)$ and $B (5, 7)$ and lie on a circle with center $O (2, − 3 y)$ lie on a circle with center , then the value of $y$ , then the value of is ____.

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Detailed Solution

If point

A (− 1, y)

and

B (5, 7)

lie on a circle with center

O (2, − 3 y)

, then the value of

y

is -1.
We have been given two points

A (− 1, y) B (5, 7)

and center

O (2, − 3 y)

.
Using the midpoint formula,

(x, y) = x 1 + x 2 2, y 1 + y 2 2

The point C(x,y) is at the exact opposite end corresponding to point B.
Substituting

x_{1} = x, x_{2} = 5, y_{1} = y, and y_{2} = 7,

in the formula,

(2, − 3 y) = x + 5 2, y + 7 2

On comparing the coordinate of y-axis, we get,

− 3 y = y + 7 2

On solving further,
y = -1
Therefore, the value of y is -1.

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