Question

The two circles x² + y² – 2x + 6y + 6 = 0, and

x² + y² – 5x + 6y + 15 = 0 touch each other. The equation of their common tangent is –

• A. x = 3
• B. y = 6
• C. 7x – 12y – 21 = 0
• D. 7x + 12y + 21 = 0

Answer 1

Answer: (A)

x = 3

Answer 2

S = x² + y² – 2x + 6y + 6 = 0 ...(1)

S´ = x² + y² – 5x + 6y + 15 = 0 ...(2)

By (1) Ž $\left\{ \begin{array} { l } \mathrm { C } _ { 2 } ( 5 / 2 , - 3 ) \\ \mathrm { r } _ { 2 } = 1 / 2 \end{array} \right.$

Q C₁C₂ = 3/2 & r₁ + r₂ = 2 + $\frac { 1 } { 2 }$ = $\frac { 5 } { 2 }$

|r₁ – r₂| = |2 – 1/2|| = 3/2

\ eq. of common tangent at point T₂ is

Ž S – S´ = 0 Ž 3x – 9 = 0 Ž x = 3