coordinate problem.

Question

Find the point on the line x= 1 where the circle with equation 2x^2 + 2y^2 - 5x + 7y - 36 = 0 intersect.

Answer 1

We know that the x value of the point(s) of intersection will be equal to "1".

Therefore, substituting 1 into the given equation of the circle we have: 2y² + 7y - 39 = 0

Solving for the zeroes of that polynomial we get: 3 and -13/2

Therefore there are two points of intersection of the line x = 1 and the circle.

The two points are: (1, 3) and (1, -13/2)