18) A light ray gets reflected from the x=-2. If the reflected ray touches the circle `x^2 + y^2 = 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) y+x+6-0

Options

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

Answer

1

Explanation

Any tangent of `x^(2)+y^(2)=4` is `y= mx +- 2 sqrt(1+mk^(2))`. If it passes through `(- 2, -4)`, then
or `4m^(2)-4)^(2)=4(1+m^(2))`
or `4m^(2)+16-16m= 4+4m^(2)`
or `m = oo, m= (3)/(4)`
Hence, the slope of the reflected ray is `3//4`
Thus, the equation of the incident rays is
`(y+4)= -(3)/(4) (x+2) ` i.e., `4y+3x+22=0`