Question

if a(-5,-2)and b(5,-4) are end ofdiameter of a circle then center of circle is

Answer 1

Answer:

(0 , -3)

Step-by-step explanation:

Given,

Co-ordinates of ends of a Diameter of a Circle :-

A = ( - 5 , - 2)

B = (5 , - 4)

To Find :-

Co-ordinates of a Circle.

Solution :-

Let, the Co-ordinates of center a Circle " C = (x , y)

According to Question , We can say that :-

Centre of the circle = Mid point of Ends of Diameter of the Circle.

$\implies 'C'\:is\;the\:Mid-point\:of\:AB$

Mid -Point formula :-

$M = \bigg(\dfrac{x_1+x_2}{2},\dfrac{y_1+y_2}{2}\bigg)$

Let's do :-

$(x , y) = \bigg(\dfrac{-5+5}{2},\dfrac{-2-4}{2}\bigg)$

$(x,y)=\bigg(\dfrac{0}{2},\dfrac{-6}{2}\bigg)$

$(x,y) = (0,-3)$

$\implies x=0\:and\:y=-3$

The co-ordinates of Centre of a Circle 'C' = (x , y) = (0 , -3)