Question

The equation of a line parallel to the line $3x+4y=0$ and touching the circle $x^2+y^2=9$ in the first quadrant is

• A. $3x+4y=15$
• B. $3x+4y=45$
• C. $3x+4y=9$
• D. $3x+4y=27$

Answer 1

The correct option is A $3x+4y=15$

Equation of line parallel to $3x+4y=0$ is given by, $3x+4y=k$

Now if above line touches the given circle, its distance from centre of the circle should be same as radius

$\Rightarrow \left|\frac{0-k}{\sqrt{3^2+4^2}}\right|=3$

$\Rightarrow k=\pm 15$

For tangent to lie in first quadrant $k>0$

Hence the required line is $3x+4y=15$