# Intersecting Points of a Circle and a Secant

How to find the intersecting points of a circle and a secant: example and its solution.

## Example

To find the intersecting points,

solve the system of equations:*x*^{2} + *y*^{2} = 25*y* = *x* - 1

Put *y* = *x* - 1 into the circle's *y*.

Substitution method

Solve the quadratic equation by factoring.

Then *x* = 4, -3.

Put *x* = 4, -3 into *y* = *x* - 1.

Then *y* = 3, -4.

So the intersecting points are (4, 3) and (-3, -4).

You can see that

the intersecting points of *x*^{2} + *y*^{2} = 25 and *y* = *x* - 1

are (4, 3) and (-3, -4).