# geometry

The graph of 2x − y= 7 is a line. The graph of x^2− 10x + y^2 + 4x = −4 is a circle. The line intersects the circle in two points. Find the coordinates of these two points.

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1. 2x − y= 7 ......(1)

x^2− 10x + y^2 + 4x = −4 .....(2)

From 1
y=(2x-7)....(3)

y²+x²-6x=-4

(2x-7)²+x²-6x=-4

4x²-28x+49+x²-6x=-4

5x²-34x+53=0

x=[34±√(1156-1060)]/10

x=[34±√96]/10

X=[34±4√6]/10

x=(17±2√6]/5

X=(17-2√6)/5 or (17+2√6)/5

When x=(17-2√6)/5

Y=2[(17-2√6)/5-7=(34-4√6)/5-7

=(34-4√6-35))/5=-(1+4√6)/5

If x=(17+2√6)/5
What would be y?

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2. I have feeling that the circle x^2− 10x + y^2 + 4x = −4 should have been
x^2− 10x + y^2 + 4y = −4, (why would you have two x terms ?)

then subbing in y=(2x-7)
x^2 - 10x + (2x-7)^2 + 4(2x-7) = -4
x^2 - 10x + 4x^2 - 28x + 49 + 8x - 28 + 4 = 0
5x^2 -30x + 25 = 0
x^2 - 6x + 5 = 0
(x - 1)(x - 5) = 0
x = 1 or x = 5
if x=1, then y = -5
if x=5, then y = 3

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