Circle And System Of Circles Question 325

Question: The straight line $ x-y-3=0 $ touches the circle $ x^{2}+y^{2}-4x+6y+11=0 $ at the point whose co-ordinates are

[MP PET 1993]

Options:

A) $ (1,-2) $

B) $ (1,,2) $

C) $ (-1,,2) $

D) $ (-1,-2) $

Show Answer

Answer:

Correct Answer: A

Solution:

Trick: The point must satisfy the line and the circle simultaneously. Obviously the point of contact is $ (1,\ -2) $ .