Circle And System Of Circles Question 16

Question: If the centre of a circle is (2, 3) and a tangent is $ x+y=1 $ , then the equation of this circle is

[RPET 1985, 89]

Options:

A) $ {{(x-2)}^{2}}+{{(y-3)}^{2}}=8 $

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

C) $ {{(x+2)}^{2}}+{{(y+3)}^{2}}=2\sqrt{2} $

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

Show Answer

Answer:

Correct Answer: A

Solution:

Find the radius by finding perpendicular distance from centre of the circle on the tangent and then find the equation of circle.