Question

The slope m of a tangent through the point (7, 1) to the circle $x^2+y^2=25$ satisfies the equation

• A. $12m^2$ + 7m - 12 = 0
• B. $12m^2$ + 7m + 9 = 0
• C. $12m^2$ - 7m - 12 = 0
• D. $9m^2$ + 12m + 16 = 0

Answer 1

The correct option is C $12m^2$ - 7m - 12 = 0

Equation of a tangent to $x^2+y^2$ = 25 is y = mx $\pm$ 5$\sqrt{1+m^2}$
This passes through (7, 1) $\Rightarrow$ 1 = 7m $\pm$ 5$\sqrt{1+m^2}$
$\Rightarrow (1-7m{)}^2=25(1+m^2)$ $\Rightarrow 49m^2-14m+1=25+25m^2$ $\Rightarrow 24m^2-14m-14=0$
$\Rightarrow 12m^2$ - 7m - 12 = 0