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Question

Find the value of λ for which the equation (10x5)2+(10y7)2=λ2(5x+12y+7)2 represents the equation of parabola.

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Solution

(10x5)2+(10y7)2=λ2(5x+12y+7)2
(x510)2+(y710)2=λ2100(5x+12y+7)2
(x510)2+(y710)2=λ2×169100(5x+12y+752+122)2
(x12)2+(y710)2=169100|λ|∣ ∣5x+12y+752+122∣ ∣
Distance from point Perpendicular distance from line
For a Parabola, Distance from point equals
perpendicular distance from line.
|λ|169100=1
|λ|=1013
λ=±10/13

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