First slide

Definition of a circle

Question

A straight line with slope 2 and y-intercept 5 touches the circle. $x^{2} + y^{2} + 16 x + 12 y + c = 0$ at a point Q. then the co-ordinates of Q are

Moderate

A

$(- 6, 11)$
B

$(- 9, - 13)$
C

$(- 10, - 15)$
D

$(- 6, - 7)$

Solution

Let $Q = (x_{1}, y_{1})$ . Then
we have $y_{1} = 2 x_{1} + 5$ and $\frac{y_{1} + 6}{x_{1} + 8} \times 2 = - 1$
$\Rightarrow x_{1} = - 6$ and $y_{1} = - 7$

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