Question

Find the equation of circle whose radius is 5 and which touches the circle x² +y² – 2x – 4y – 20 =0 at the point (5, 5).

• A. x² + y² – 18x – 16y + 120 =0
• B. x² + y² + 6x – 3y - 54 =0
• C. x² + y² – 17x – 19y + 50 =0
• D. x² + y² – 18x – 8y + 60 =0

Answer 1

The correct option is A x² + y² – 18x – 16y + 120 =0

The given circle is x² +y² – 2x – 4y – 20 =0 with centre (1, 2) and radius = = 5

And required circle has radius 5 hence circles touch each other externally.

Since point of contact is P(5, 5).

P is the mid point of C₁ and C₂, let co – ordinate of centre C₂ is (h, k) then

= 5; h = 9

= 5; k = 8

And, Equation of required circle is

x² + y² – 18x – 16y + 120 =0; Option(a)