In how many points do the graphs of the equations x^2 + y^2 = 25 and y^2 = 4x intersect?

You need to remember that the coordinates of points that
lie on both curves need to be solutions of both
given equations.

You need to express   in terms of
  in the equation such that:

25 - x^2

You need to set the equations  
and equal such that:

4x

+ 4x - 25 = 0

You should complete the square such
that:

0

= 29 =gt x+2 = +-sqrt29

sqrt29

sqrt29

You need to find the coordinates   and  
such that:

+-sqrt(4(sqrt29-2))

+-sqrt(4(-sqrt29-2))

Hence, evaluating the
coordinates of points of intersection of curves yields
+-sqrt(4(sqrt29-2))x_2 = -2 - sqrt29 ; y_(3,4) = +-sqrt(4(-sqrt29-2)).