How to graph $|z+1| + |z-7| = 10$? Please help me.

Question

The solution indicated that it is a oval , center $(3,0)$ and $a = 10/2 $.

Answer 1

This is to say that the sum of the radii $\underbrace{|z+1|}_{r_1}+\underbrace{|z-7|}_{r_2}=\underbrace{10}_{2a},$ according to the definition on Wolfram Mathworld http://mathworld.wolfram.com/Ellipse.html

Answer 2

Hint: You can see it as an ellipse with focuses $(-1,0)$ and $(7,0)$ and $a=10/2$.