A ray emanating from (6,2) is incident on ellipse ((x-1)2/45)+((y-2)2/20)=1 at (4,6). The equation of reflected ray (after 1 text st reflection) is

Question

A ray emanating from (6,2) is incident on ellipse ((x-1)2/45)+((y-2)2/20)=1 at (4,6). The equation of reflected ray (after 1 text st reflection) is (A) x-2 y+8=0 (B) x+2 y+8=0 (C) x+2 y-8=0 (D) x-2 y-8=0

Tardigrade Admin · Accepted Answer

(6,2) is a focus ∴ the reflected ray passes through the other focus i.e. the point (-4,2) ∴ equation of the reflected ray y-6=(4/8)(x-4) i.e. x-2 y+8=0

Q. A ray emanating from $(6, 2)$ is incident on ellipse $\frac{( x - 1 ) ^{2}}{45} + \frac{( y - 2 ) ^{2}}{20} = 1$ at $(4, 6)$ . The equation of reflected ray (after $1^{st}$ reflection) is

$x - 2 y + 8 = 0$

$x + 2 y + 8 = 0$

$x + 2 y - 8 = 0$

$x - 2 y - 8 = 0$

$(6, 2)$ is a focus
$∴$ the reflected ray passes through the other focus
i.e. the point $(- 4, 2)$
$∴$ equation of the reflected ray $y - 6 = \frac{4}{8} (x - 4)$
i.e. $x - 2 y + 8 = 0$

Q. A ray emanating from (6,2) is incident on ellipse 45(x−1)2​+20(y−2)2​=1 at (4,6). The equation of reflected ray (after 1st reflection) is

x−2y+8=0

x+2y+8=0

x+2y−8=0

x−2y−8=0