Question

A light ray gets reflected from the line x = –2.If the reflected ray touches the circle x² + y² = 4 and point of incident is

(–2, –4), then equation of incident ray is-

• A. 4y + 3x + 22 = 0
• B. 3y + 4x + 20 = 0
• C. 4y + 2x + 20 = 0
• D. x + y + 6 = 0

Answer 1

Answer: (A)

4y + 3x + 22 = 0

Answer 2

Any tangent of x² + y² = 4 is y = mx ± 2$\sqrt{1 + m^{2}}$. If it passes through (–2, –4), then (2m – 4)² = 4 (1 + m²) .

Ž 4m² + 16 – 16m = 4 + 4m²

Ž m = , m = $\frac{3}{4}$

Also, m =  as x = –2 is reflected ray. Hence slope of reflected ray is $\frac{3}{4}$. Thus equation of incident ray is

(y + 4) = –$\frac{3}{4}$ (x + 2)

Ž 4y + 3x + 22 = 0

Hence (1) is the correct answer.