SOLUTION: Sketch the circle whose equation is x2 + y2 = 100. Using the same system of coordinate axes, graph the line x + 3y = 10, which should intersect the circle twice — at A = (10, 0)
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-> SOLUTION: Sketch the circle whose equation is x2 + y2 = 100. Using the same system of coordinate axes, graph the line x + 3y = 10, which should intersect the circle twice — at A = (10, 0)
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Question 1154276: Sketch the circle whose equation is x2 + y2 = 100. Using the same system of coordinate axes, graph the line x + 3y = 10, which should intersect the circle twice — at A = (10, 0) and at another point B in the second quadrant. Estimate the coordinates of B. Now use algebra to find them exactly. Segment AB is called a chord of the circle.
You can put this solution on YOUR website! The graph of the two equations, x^2 +y^2 = 100 and x +3y = 10 is
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Using the graph, estimate the second point to be (-8, 6)
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solve both equations for y
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y = sqrt(100 -x^2)
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y = -x/3 +10/3
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set them equal to each other
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sqrt(100 -x^2) = -x/3 +10/3
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square both sides
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100 -x^2 = x^2/9 -20x/9 +100/9
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multiply both sides of = by 9
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900 -9x^2 = x^2 -20x +100
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10x^2 -20x -800 = 0
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divide both sides of = by 10
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x^2 -2x -80 = 0
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(x-10) * (x+8) = 0
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therefore x = 10, x = -8
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We know y^2 = 100 -x^2 from the first given equation
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y^2 = 100 -(-8)^2 = 36
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y = + or - 6
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Since B is in the second quadrant, B = (-8, 6)
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