An incident ray is reflected by the line mirror y = 1 at the point (2, 1). If the reflected ray touches the circle x2 + y2 = 1, then the equation of incident ray is

Engineering

Mathematics

Tangent and Normal to Circle

Question

An incident ray is reflected by the line mirror y = 1 at the point (2, 1). If the reflected ray touches the circle x² + y² = 1, then the equation of incident ray is

3x – 4y – 2 = 0

3x + 4y – 10 = 0

4x – 3y – 5 = 0

4x + 3y – 11 = 0

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Equation of the ray:
y – 1 = m(x – 2)
∵ mx – y – 2m + 1 = 0
touches the circle
∴   p = r
$| \frac{1 - 2 m}{\sqrt{1 + m^{2}}} |$ = 1
1 + 4m² – 4m = 1 + m²
∵ m ≠ 0
4m – 4 = m
m = $\frac{4}{3}$         tanα = $\frac{4}{3}$
tan(π – α) = – $\frac{4}{3}$
∴   Equation of incident ray
y – 1 = $\frac{4}{3}$ – (x – 2)
3y – 3 = – 4x + 8
4x + 3y = 11

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