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10 votes
Y=x+16
X^2+y^2=128
Find the intersection of the line and the circle

User Lars P
by
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1 Answer

9 votes

Answer:

(-8, 8)

Explanation:

Plug in the y from the top equation into the y of the bottom equation

x² + (x + 16)² = 128

x² + x² + 32x + 256 = 128

Subtract 128 from both sides to make it equal to zero

2x² + 32x + 256 = 128

- 128 - 128

2x² + 32x + 128 = 0

Divide both sides by 2

(2x² + 32x + 128)2 = 0/2

x² + 16x + 64 = 0

Factor the equation

(x + 8)(x + 8) = 0

We see that x will have to be -8 for it to equal zero

so x = -8

Plug the new x into one of the original equations; let's use the top one

y = -8 + 16

y = 8

User ExAres
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