How many points of intersection are there for x-y=2 and x^2+y^2=25 ?
A circle is the set of all points that are the same distance, r, from a fixed point.
General Formula:
x ^ 2 + y ^ 2 = r ^ 2
where r is the radius
In this case :
x ^ 2 + y ^ 2 = 25 = 5 ^ 2
The circle has a center of (0,0) and a radius of 5
x - y = 2
x - 2 = y
y = x - 2
The straight line.
Points of intersection:
x ^ 2 + y ^ 2 = 25
Substitute y = x - 2
x ^ 2 + ( x - 2 ) ^ 2 = 25
x ^ 2 + ( x ^ 2 - 2 * x * 2 + 2 ^ 2 ) = 25
x ^ 2 + ( x ^ 2 - 4 * x + 4 ) = 25
x ^ 2 + x ^ 2 - 4 * x + 4 = 25
2 x ^ 2 - 4 x + 4 - 25 = 0
2 x ^ 2 - 4 x - 21 = 0
If you don't know how to solve this equation in google type:
quadratic equation online
When you see list of results click on:
Free Online Quadratic Equation Solver:Solve by Quadratic Formula
When page be open in rectangle type:
2 x ^ 2 - 4 x - 21 = 0
and click option: solve it
You will see solution step-by step
So solutions are :
x = 1 + sqrt ( 23 / 2 ) = 4.39116
y = x - 2 = 1 + sqrt ( 23 / 2 ) - 2 =
sqrt ( 23 / 2 ) - 1 = 2.39116
and
x = 1 - sqrt ( 23 / 2 ) = - 2.39116
y = x - 2 = 1 - sqrt ( 23 / 2 ) - 2 =
- 1 - sqrt ( 23 / 2 ) - 1 = - 4.39116
If you want to see graph in google type:
functions graphs online
When you see list of results click on:
rechneronline.de/function-graphs/
When page be open in blue recatangle type:
(25-x^2)^0.5
In gray recatangle type:
-(25-x^2)^0.5
In white recatangle type:
x-2
And click option :
Draw
You will see 2 points of intersection.