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Parametric Equation of Tangent

Tangent drawn...

Question

Tangent drawn at any point on $y^{2} = 4 a x$ meets the axis of parabola at $T$ and tangent at vertex at $S$ . If $T A S G$ is a rectangle, where $A$ is the vertex, then locus of $G$ is

y^{2} = a x

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y^{2} = - a x

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y^{2} = 2 a x

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y^{2} = - 2 a x

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Solution

The correct option is B $y^{2} = - a x$

Given parabola $y^{2} = 4 a x$
Equation of tangent is $t y = x + a t^{2}$

$x = 0 \Rightarrow S \equiv (0, a t) y = 0 \Rightarrow T \equiv (- a t^{2}, 0)$
$(h, k) = (- a t^{2}, a t)$
Then the locus of $G$ is
$h = - a {(\frac{k}{a})}^{2} ∴ y^{2} = - a x$

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Q. Tangent drawn at any point on

y^{2} = 4 a x

meets the axis of parabola at

T

and tangent at vertex at

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. If

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Parametric Equation of Tangent

Standard XI Mathematics

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Tangent drawn at any point on y2=4ax meets the axis of parabola at T and tangent at vertex at S. If TASG is a rectangle, where A is the vertex, then locus of G is

The correct option is B y2=−ax Given parabola y2=4ax Equation of tangent is ty=x+at2 x=0 ⇒S≡(0,at)y=0 ⇒T≡(−at2,0) (h,k)=(−at2,at) Then the locus of G is h=−a(ka)2∴y2=−ax

Tangent drawn at any point on $y^{2} = 4 a x$ meets the axis of parabola at $T$ and tangent at vertex at $S$ . If $T A S G$ is a rectangle, where $A$ is the vertex, then locus of $G$ is

The correct option is B $y^{2} = - a x$

Given parabola $y^{2} = 4 a x$
Equation of tangent is $t y = x + a t^{2}$

$x = 0 \Rightarrow S \equiv (0, a t) y = 0 \Rightarrow T \equiv (- a t^{2}, 0)$
$(h, k) = (- a t^{2}, a t)$
Then the locus of $G$ is
$h = - a {(\frac{k}{a})}^{2} ∴ y^{2} = - a x$