Question

The equations to the tangents to the circle $x ^ { 2 } + y ^ { 2 } - 6 x + 4 y = 12$ which are parallel to the straight line 4x+3y+5=0, are

• A. $3 x - 4 y - 19 = 0 , \quad 3 x - 4 y + 31 = 0$
• B. $4 x + 3 y - 19 = 0 , \quad 4 x + 3 y + 31 = 0$
• C. $4 x + 3 y + 19 = 0 , \quad 4 x + 3 y - 31 = 0$
• D. $3 x - 4 y + 19 = 0 , \quad 3 x - 4 y + 31 = 0$

Answer 1

Answer: (C)

$4 x + 3 y + 19 = 0 , \quad 4 x + 3 y - 31 = 0$

Answer 2

Let equation of tangent be $4 x + 3 y + k = 0$ then

$\sqrt { 9 + 4 + 12 } = \left| \frac { 4 ( 3 ) + 3 ( - 2 ) + k } { \sqrt { 16 + 9 } } \right|$

⇒ $6 + k = \pm 25 \Rightarrow k = 19$ and – 31

Hence the equations of tangents are $4 x + 3 y - 31 = 0$