Question

Two circles, each of radius 5 units, touch each other at (1, 2). If the equation of their common tangent is 4x + 3y – 10 = 0, then equation of one such circle is-

• A. x² + y² – 6x + 2y + 15 = 0
• B. x² + y² – 10x – 10y + 25 = 0
• C. x² + y² + 6x – 2y – 15 = 0
• D. x² + y² – 10x – 10y – 25 = 0

Answer 1

Answer: (B)

x² + y² – 10x – 10y + 25 = 0

Answer 2

Equation of circles will be

(x – 1)² + (y – 2)² + l (4x + 3y – 10) = 0

Ž x² + y² + 2x (2l – 1) + y (3l – 4) + 5 – 10l = 0

It’s radius is ‘5’ units.,

Ž (2l – 1)² + $\frac{1}{4}$ (3l – 4)² – 5 + 10l = 25

Ž l = ± 2.

Thus equation of circles are

x² + y² + 6x + 2y – 15 = 0

or x² + y² – 10x – 10y + 25 = 0.

Hence (2) is the correct answer.