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Tangent To Parabola

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Prove that image of the focus lies on directrix with respect to any tangent of parabola y^(2)=4ax

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Equation of common tangent of parabola y ^(2) = 8x and x ^(2) + y =0 is

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A line is tangent to a parabola if it intersects the parabola at not more than one point.

the tangent to a parabola are x-y=0 and x+y=0 If the focus of the parabola is F(2,3) then the equation of tangent at vertex is

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Tangents of a parabola

Tangents of a parabola