CircleHardBloom L3
Question
A straight line with slope 2 and $y$-intercept 5 touches the circle, $x^{2} + y^{2} + 16x + 12y + c = 0$ at a point $Q$. Then the coordinates of $Q$ are:
Options
A.$( - 6,11)$
B.$( - 9, - 13)$
C.$( - 6, - 7)$
Solution
[Key Concept: A line is tangent to a circle iff the centre's distance equals the radius — impose it on $y = 2x + 5$.]
$\left. \ y_{1} = 2x_{1} + 5\ \right\rbrack$
and $\frac{\left( y_{1} + 6 \right)}{x_{1} + 8} \times 2 = - 1$
$\Rightarrow \ x_{1} = - 6$ and $y_{1} = - 7$
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