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GB-20-05-001 · Intersections of a line and circle

Solve the simultaneous equations
x2+y2=290x^2+y^2=290
y=17y=17

Simultaneous Equations: Circle & Line Booklet p. 28 & p. 83
Method
1) Substitute the given y value into the circle equation
2) Isolate x²
3) Take both square roots and give both coordinate pairs
Worked Example (GB-20-05-001)
1)
Substitute y=17y=17 into the circle equation: x2+(17)2=290x^2+(17)^2=290.
2)
x2=290−289=1x^2=290-289=1
3)
Take both square roots: x=±1=±1x=\pm\sqrt{1}=\pm1. Pair each with y=17y=17.
Ans = (x,y)=(1,17)(x,y)=(1,17) or (−1,17)(-1,17)