A) (1, 10)
B) (4, 7)
C) (7,7)
D) (9, V19)
Correct Answer: D
Solution :
Here, it is given that the circle with centr at origin passes through the point \[(-8,-6)\]. The distance from origin \[(0,0)\] to point \[(-8,-6)\] will be the radius of the given circle. So, by distance formula, Radius of circle \[=\sqrt{{{(-8-0)}^{2}}+{{(-6-0)}^{2}}}\] \[=\sqrt{{{8}^{2}}+{{6}^{2}}}\] \[=\sqrt{64+34}=\sqrt{100}=10.\] Now, any point that lies on the circle will be at the same distance as that of radius. Hence, check the options whether any point has the same distance from the origin as radius of the circle. Option gives \[\sqrt{{{(9-0)}^{2}}+{{(\sqrt{19}-0)}^{2}}}=\sqrt{81+19}\] \[=\sqrt{100}=10.\] Hence, the distance of point \[(9,\,\sqrt{19})\] from the origin is same as that of radius equal to 10. The circle given passes through the point \[(9,\,\sqrt{19})\].
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