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Question 1071339: Please explain how you do this question: Derive the equation of the locus of a point P(x,y) which moves so that its distance from (2,3) is always equal to its distance from the line x+2=0
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Please explain how you do this question: Derive the equation of the locus of a point P(x,y) which moves so that its distance from (2,3) is always equal to its distance from the line x+2=0
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The locus is a parabola.
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Plot the point (2,3); that is the focus of the parabola.
Sketch the line x = -2; that is the directrix
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Distance from directrix to focus = 5
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The vertex is at (2,1/2)
p = 3-(1/2) = 5/2
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Equation:
Form:: (x-h)^2 = 4p(y-k)
(x-2)^2 = 4(5/2)(y-(1/2)
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x^2 - 4x + 4 = 10y - 5
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y = (1/10)x^2 - (2/5)y + (9/10)
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Cheers,
Stan H.
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