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

Question

asked Oct 7, 2022 57.3k views

2 Answers

Coulix · Answer 1 · 2022-10-14T07:04:18+0000

Answer:

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

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

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

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

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

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

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