A ray emanating from the point (–4, 0) is incident on the ellipse mirror 9x² + 25y² = 225 at the point P with abscissa 3. Then equation of the reflected ray after first reflection is ax + by = c. HCF of a, b, c is 1 then |b| is

 $$\begin{gathered} Given ellipse \frac{x^2}{25}+\frac{y^2}{9}=1 \\ where a^2=25,b^2=9 and e=\frac{4}{5} \\ focus=(-ae,0)=(-4,0) \\ It means given point is focus \\ We know that rays emanating from the one focus passes \\ through other focus (4,0) \\ Let P=(3,y_1) \\ sub P in ellipse we get y_1=\pm \frac{12}{5} \\ So, Equation of reflected ray is y=\frac{\pm \frac{12}{5}}{-1}(x-4) \\ \Rightarrow 12x-5y-48=0 or 12x+5y=48 \\ wherea=12,b=-5 ,c=48 \\ Now \left|b\right|=5(\because H.C.F of a,b,c=1) \end{gathered}$$