Question

Find the center of a circle whose end points of a diameter are A (-5,6) and B (3,4)

Answer 1

The center co - ordinates of the circle will be (-1, 5) .

To find the center co-ordinates of a given circle :

Given

The end points of a diameter of a circle are:

$(x_{1} , y_{1}) = (-5 , 6)$

$(x_{2} , y_{2}) = (3 , 4)$

As we know,

Mid points of X- axis :

$X = \frac{x_{1} + x_{2} }{2}$

On putting the values, we get:

$X = \frac{-5 + 3}{2}$

$X = \frac{-2}{2}$

$X = -1$

Mid points of Y- axis :

$Y = \frac{y_{1} + y_{2} }{2}$

On putting the values, we get:

$Y = \frac{6 + 4}{2}$

$Y = \frac{10}{2}$

$Y = 5$

Therefore, the center co-ordinates of a circle are (-1, 5).

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On putting the values, we get