Solve Simultaneous Equations One Linear, one quadratic [Circle]

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Solve Simultaneous EquationsOne Linear, one
quadratic Circle

• GCSE Higher

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Content

• Equation of a circle
• Equation of straight line
• Graphical Solution
• Algebraic Solution Substitution Method

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Equation of a Circle

• Is x2 y2 r2
• Where
• The circle has centre (0,0)
• Its radius is r

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Consider x2 y2 9
When y 0, x2 9 So x 3 or -3
When x 0, y2 9 So y 3 or -3
x
x
x
We have 2 points (3,0)
We have 2 points (0,3)
and (0,-3)
and (-3,0)
x
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Equation Straight Line

• y mx c
• Where
• m is the gradient or slope
• c is the y-intercept

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Consider y 2x 1
y intercept
Point (0,1)
x
Gradient 2
Line rises 2 units for every 1 unit to the right
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Solve these 2 equations simultaneously

• Graphical method
• May be required to draw one or both equations
• Careful drawing required for accurate answer

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. Once drawn
1st Solution x 0.94 y 2.85
2nd Solution x -1.75 y -2.41
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Algebraic Solution
y 2x 1
x2 y2 9
x2 (2x 1)2 9
Substitute 2x 1 for y
x2 4x2 4x 1 9
Expand (2x 1)2
5x2 4x 1 9
Simplify
5x2 4x -8 0
Rearrange
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Use formula
5x2 4x -8 0
So, x -1.7266. or 0.9266.
So, y -2.453. or 2.8532.
Solutions, (-1.73, -2.45) (0.93,2.85) to
2d.p.