Question

The equation of the line parallel to the line 3x + 4y = 0 and touching the circle x² + y² = 9 in the first quadrant is –

• A. 3x + 4y = 9
• B. 3x + 4y = 45
• C. 3x + 4y = 15
• D. None of these

Answer 1

Answer: (C)

3x + 4y = 15

Answer 2

x² + y² = 9 ...(1)

3x + 4y = 0 ...(2)

Equation of the line parallel to the line (2) is

Ž 3x + 4y + l = 0 ...(3)

Q line (3) touches the circle (1)

Ž CM = 8 Ž CM = $\left| \frac { 0 + 0 + \lambda } { 5 } \right|$ = 3 Ž l = ± 15

By (3) Ž equation of tangent is Ž 3x + 4y = 15