Find the locus of a point which moves such that the ratio of its distance from the point $(-5,0)$ to its distance from the line $5x+ 16 = 0$ is $5/4$.
I was trying this question, and I got my answer $x= -16/5$. I don't know how to combine the equation, but I know that its eccentricity is $5/4$. I was not able to find the locus of moving point. I don't know from where I have to start.
Thanks to anybody who can help me.