Intersecting Points of a Circle and a Secant

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

Find the coordinates of the intersecting points of the circle x^2 + y^2 = 25 and the line y = x - 1.

To find the intersecting points,
solve the system of equations:
x2 + y2 = 25
y = x - 1

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

Substitution method

Square of a difference

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 x2 + y2 = 25 and y = x - 1
are (4, 3) and (-3, -4).