SOLUTION: A circle is centered at the origin and has a radius of √5 units. A line with a slope of 2 passes through the origin and intersects the circle in two places. Where does the line

Question 1169814: A circle is centered at the origin and has a radius of √5 units. A line with a slope of 2 passes
through the origin and intersects the circle in two places. Where does the line intersect the
circle?
This is the last question that Im struggling please help me
Found 2 solutions by josgarithmetic, MathTherapy:
Answer by josgarithmetic(39620) (Show Source): You can put this solution on YOUR website!
The circle equation accordingly is .
The line described has equation .
Now you should know what to do. Try, substitute for y.
Answer by MathTherapy(10553) (Show Source): You can put this solution on YOUR website!

A circle is centered at the origin and has a radius of √5 units. A line with a slope of 2 passes
through the origin and intersects the circle in two places. Where does the line intersect the
circle?
This is the last question that Im struggling please help me

.
m (slope) = 2 ; Point (0, 0)
Equation of line that passes through origin (also center of circle): y = 2x
Equation of circle:
We now have the following system of equations:
------- Substituting 2x for y in eq (ii)

x = 1 x = - 1
y = 2x y = 2x
y = 2(1) = 2 y = 2(- 1) = - 2
Intersection: (1, 2) Intersection: (- 1, - 2)
Therefore, the line intersects the circle at (see above diagram).
NOTE that the equation of the line: y = 2x "states" that the value of the y-coordinate is TWICE that of the x=coordinate.
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