Answer:
[tex] a=1.58, \: \: a =-7.58[/tex]
Step-by-step 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).
[tex] [0-(-3)]^2 + [-6-(-2)]^2=[a-(-3)]^2 + [0-(-2)]^2[/tex]
[tex] [0+3]^2 + [-6+2]^2=[a+3]^2 + [0+2]^2[/tex]
[tex] [3]^2 + [-4]^2=[a+3]^2 + [2]^2[/tex]
[tex] 9 + 16=[a+3]^2 + 4[/tex]
[tex] 25=[a+3]^2 + 4[/tex]
[tex] 25-4=[a+3]^2[/tex]
[tex] 21=[a+3]^2[/tex]
[tex] [a+3]^2=21[/tex]
[tex] [a+3]=\pm\sqrt {21} [/tex]
[tex] a=\pm\sqrt {21} - 3[/tex]
[tex] a=\sqrt {21} - 3, \: \: a =-\sqrt {21} - 3[/tex]
[tex] a=1.58257569, \: \: a =-7.58257569[/tex]
[tex] a=1.58, \: \: a =-7.58[/tex]
