First slide

Definition of a circle

Question

A light ray reflected from $x = - 2 . If the reflected ray$ $touches the circle x^{2} + y^{2} = 4 and the point of incident is$
$(- 2, - 4), then the equation of incedents ray$

Moderate

A

$4 y + 3 x + 22 = 0$
B

$3 y + 4 x + 20 = 0$
C

$4 y + 2 x + 20 = 0$
D

$y + x + 6 = 0$

Solution

$Any tangent of x^{2} + y^{2} = 4 is y = m x \pm 2 \sqrt{1 + m^{2}} . If it passes through (- 2, - 4), then$
$(2 m - 4)^{2} = 4 (1 + m^{2})$
$or 4 m^{2} + 16 - 16 m = 4 + 4 m^{2}$

$or m = \infty, m = \frac{3}{4}$
Hence, the slope of the reflected ray is 3/4.
Thus, the equation of the incident ray is
$(y + 4) = - \frac{3}{4} (x + 2) i.e., 4 y + 3 x + 22 = 0$

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