A ray emanating from the point `(- 4, 0)` is incident on the ellipse `9x^2 + 25y^2 =225` at the point `P` abscissa `3.` Find the equation of the reflected ray after first reflection.

Options

A. `(-15,sqrt63)`
B. `(-15/4,sqrt63/4)`
C. `(-15/4,sqrt63/4)`
D. `(-15/2,sqrt63/2)`

Answer

C

Explanation

Eqation of ellipse is `9x^(2)+25y^(2)=225 or (x^(2))/(25)+y^(2)/(9)=1`
`Here, a=5,b=3
now `pf_1=4pf_2`
`therefore pf_1+pf_2=5pf_2,2a=5pf_2`
`10=5pf_2 rArr 2=pf_2`
now, c^(2)=a^(2)-b^(2)=25-9=16`
` `therefore f_(1)-=(4,0),f_2-=(-4,0)`
` let the coordinates of p be (5 cos0, 3 sin 0).
` `therefore pf_(2)=2`
`rArr (5 cos0+4)^(2)+(3sin0)^(2)=4`
`rArr 16cos^(2)0+40cos0+21=0`
`rArr (4cos0+3)(4 cos0+7)=0`
`rArr cos0=-3/4 or cos0=-7/4`
`