Question

The equations of the tangents to the circle $x^2+y^2$ - 4x - 6y - 12 = 0 and parallel to 4x - 3y = 1 are

• A. 4x + 3y + 14 = 0, 4x + 3y + 16 = 0
• B. 4x – 3y – 24 = 0, 4x – 3y + 26 = 0
• C. x – y – 14 = 0, x – y + 16 = 0
• D. 4x – 3y + 34 = 0, 4x – 3y + 16 = 0

Answer 1

The correct option is B 4x – 3y – 24 = 0, 4x – 3y + 26 = 0

For the circle $x^2+y^2$ - 4x - 6y - 12 = 0, centre is (2, 3), radius = 5
Equation of a line parallel to 4x - 3y = 1 is 4x - 3y + k = 0
4x - 3y + k = 0 is a tangent to the circle $\Rightarrow$ $\frac{|4\left(2\right)-3\left(3\right)+k|}{5}$ = 5 $\Rightarrow$ $|k-1|$ = 25 $\Rightarrow$ k = 1 $\pm$ 25 $\Rightarrow$
k = 26 or - 24.
$\therefore$ Required tangents are 4x - 3y + 26 = 0, 4x - 3y - 24 = 0