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Prove that the length of the intercept o...

Prove that the length of the intercept on the normal at the point `P(at^(2),2at)` of a parabola `y^(2)=4ax` made by the circle described on the line joining the focus and P as diameter is `asqrt(1+t^(2))`.

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Prove that the length of the intercept on the normal at the point P(a t^2,2a t) of the parabola y^2=4a x made by the circle described on the line joining the focus and P as diameter is asqrt(1+t^2) .

What is the length of the focal distance from the point P(x_(1),y_(1)) on the parabola y^(2) =4ax ?

The slope of the tangent to the parabola y^(2)=4ax at the point (at^(2), 2at) is -

Prove that the normals at the points (1,2) and (4,4) of the parbola y^(2)=4x intersect on the parabola.

The equation of the normal to the parabola y^(2) =4ax at the point (at^(2), 2at) is-

Prove that the normal at (am^(2),2am) to the parabola y^(2)=4ax meets the curve again at an angle tan^(-1)((1)/(2)m) .

Find the angle at which normal at point P(a t^2,2a t) to the parabola meets the parabola again at point Qdot

Prove that the the middle points of the normal chords of the parabola y^(2)=4ax is on the curve (y^(2))/(2a)+(4a^(3))/(y^(2))=x-2a

Length of the shortest normal chord of the parabola y^2=4ax is

If the tangent at any point P to the parabola y^(2)=4ax meets the directrix at the point K , then the angle which KP subtends at its focus is-

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