Intersecting Points of a Circle and a Secant
How to find the intersecting points of a circle and a secant: example and its solution.
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.
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).