Question

A circle of center (-3 , -2) passes through the points (0 , -6) and (a , 0). Find a?

Answer 1

-4.5

Explanation:

Answer 2

`a=1.58, \: \: a =-7.58`

Explanation:

Since, circle of center (-3 , -2) is passing through the points (0 , -6) and (a , 0).

Therefore, points (0 , -6) and (a , 0) will be equidistant from the center of the circle (-3 , -2).

Hence,

Distance between (0 , -6) and (-3 , -2) = Distance between (a , 0) and (-3 , -2).

`[0-(-3)]^2 + [-6-(-2)]^2=[a-(-3)]^2 + [0-(-2)]^2`

`[0+3]^2 + [-6+2]^2=[a+3]^2 + [0+2]^2`

`[3]^2 + [-4]^2=[a+3]^2 + [2]^2`

`9 + 16=[a+3]^2 + 4`

`25=[a+3]^2 + 4`

`25-4=[a+3]^2`

`21=[a+3]^2`

`[a+3]^2=21`

`[a+3]=\pm\sqrt {21}`

`a=\pm\sqrt {21} - 3`

`a=\sqrt {21} - 3, \: \: a =-\sqrt {21} - 3`

`a=1.58257569, \: \: a =-7.58257569`

`a=1.58, \: \: a =-7.58`