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A point P(x,y) is such that its distance from the fixed point (alpha,0) is equal to its distance from y-axis. Prove that the equation of the locus is given by, y^2 = alpha (2x-alpha). |
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Answer» <P> SOLUTION : It is given that `BAR(AP) = bar(BP)` or, `sqrt((x-alpha)^2 + y^2) = x` or, `(x-alpha)^2 + y^2= x^2` or, `y^2 = x^2-x^2-alpha^2 + 2alphax = alpha(2x-alpha)` `therefore y^2 = alpha(2x-alpha)` which is the locus of the POINT P(x,y). |
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