Question

A tangent is drawn to the circle $x^2+y^2=9$ at $(3,3)$, then the equation of the line which is parallel to the tangent and passes through $(5,4)$ is

• A. $x+y=16$
• B. $x+y=9$
• C. $x+y=4$
• D. $x+y=81$

Answer 1

The correct option is B $x+y=9$

Equation of circle
$x^2+y^2=9$
Slope of the tangent at $(3,3)$
$2x+2y{y}^{\prime }=0\Rightarrow y^{\prime }=-\frac{x}{y}$
$\Rightarrow$ Slope at $(3,3)=-1$
Let the equation of the line be $y=-x+c$
Putting the point $(5,4)$ in the equation,
$4=-5+c\Rightarrow c=9$
Hence the equation of the line is given by $x+y=9$