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Equation of the tangent at a point $P$ on the parabola
$y^{2} = 4 a x$ the normal at which is at a distance
$a \sqrt{5} / 4$ from the focus of the parabola is

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detailed solution

Correct option is A

Equation of the normal with slop m isy=mx−2am−am3 whose distance from the focus(a,0) is am−2am−am31+m2=54a⇒16m21+m2=5⇒m2=1/4⇒m=±1/2Slope of the tangent is ± 2 and the equation of thetangent is y=±2x±a/2⇒4x±2y+a=0.

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Equation of the tangent at a point P on the parabola y2=4ax the normal at which is at a distancea 5 /4 from the focus of the parabola is

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Ready to Test Your Skills?

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Equation of the tangent at a point $P$ on the parabola
$y^{2} = 4 a x$ the normal at which is at a distance
$a \sqrt{5} / 4$ from the focus of the parabola is