Find the coordinate(s) of the point(s) that satisfy the following conditions:
- equidistant from the points $(4,-7)$ and $(8,5)$
- distance of 5 from the point $(-5,1)$
Find the coordinate(s) of the point(s) that satisfy the following conditions:
Hint: The distance from a point $p_1=(x_1,y_1)$ to another point $p_2(x_2,y_2)$ is given by $$d\left(p_1,p_2\right) = \sqrt{\left(x_1-x_2\right)^2+\left(y_1-y_2\right)^2}$$
Now you are searching a special point $p=(x,y)$ that fullfills
Now set up the resulting equations and solve the non-linear system for $x$ and $y$
Note that $x^2$ and $y^2$ cancels out in the first equation, so it is easy to solve this either to $x$ or $y$ and put it in the second equation.
Can you go ahead?