Circle And System Of Circles Question 365

Question: x $ y-x+3=0 $ is the equation of normal at $ ( 3+\frac{3}{\sqrt{2}},\frac{3}{\sqrt{2}} ) $ to which of the following circles

[Roorkee 1990]

Options:

A) $ {{( x-3-\frac{3}{\sqrt{2}} )}^{2}}+{{( y-\frac{\sqrt{3}}{2} )}^{2}}=9 $

B) $ {{( x-3-\frac{3}{\sqrt{2}} )}^{2}}+y^{2}=6 $

C) $ {{(x-3)}^{2}}+y^{2}=9 $

D) $ {{(x-3)}^{2}}+{{(y-3)}^{2}}=9 $

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Answer:

Correct Answer: C

Solution:

Trick: Only option (c) satisfies the given co-ordinates of the point.