Question

The difference between the radii of the largest and the smallest circles which have their centre on the circumference of hte circle $x^2+y^2+2x+4y-4=0$ and passes through the point $(a,b)$ lying outside the given circle, is

• A. $6$
• B. $\sqrt{(a+1{)}^2+(b+2{)}^2}$
• C. $3$
• D. $\sqrt{(a+1{)}^2+(b+2{)}^2}-3$

Answer 1

The correct option is A $6$

The given circle is $(x+1{)}^2+(y+2{)}^2=9$, which has radius $=3$.
The points on the circle which are nearest and farthest to the point P(a, b) are Q and R, respectively.
Thus, the circle centred at Q having radius PQ will be the smallest circle while the circle centred at R having radius PR will be the largest required circle.
Hence, difference between their radii $=PR-PQ=QR=6$.