If a tangent to the parabola y2-4ax makes an angle of -3 with the axis of symmetry of the parabola- then point of contacts is-are

The axis of symmetry of the parabola y^2=4ax is x axis Any line which makes an angle of π3 have slope m=±tanπ3=±√(3) The point of contact in slope form to parab ...

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Standard XI

Mathematics

Slope Form a Line

If a tangent ...

Question

If a tangent to the parabola $y^{2} = 4 a x$ makes an angle of $\frac{π}{3}$ with the axis of symmetry of the parabola, then point of contact(s) is/are

(\frac{a}{3}, - \frac{2 a}{\sqrt{3}})

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(3 a, - 2 \sqrt{3} a)

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(3 a, 2 \sqrt{3} a)

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(\frac{a}{3}, \frac{2 a}{\sqrt{3}})

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Solution

The correct option is D $(\frac{a}{3}, \frac{2 a}{\sqrt{3}})$
The axis of symmetry of the parabola $y^{2} = 4 a x$ is $x -$ axis
Any line which makes an angle of $\frac{π}{3}$ have slope
$m = \pm tan \frac{π}{3} = \pm \sqrt{3}$
The point of contact in slope form to parabola $y^{2} = 4 a x$ is
$\Rightarrow (\frac{a}{m^{2}}, \frac{2 a}{m}) = (\frac{a}{3}, \pm \frac{2 a}{\sqrt{3}})$

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Slope Form a Line

Standard XI Mathematics

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If a tangent to the parabola y2=4ax makes an angle of π3 with the axis of symmetry of the parabola, then point of contact(s) is/are

The correct option is D (a3,2a√3)The axis of symmetry of the parabola y2=4ax is x−axis Any line which makes an angle of π3 have slope m=±tanπ3=±√3 The point of contact in slope form to parabola y2=4ax is ⇒(am2,2am)=(a3,±2a√3)

If a tangent to the parabola $y^{2} = 4 a x$ makes an angle of $\frac{π}{3}$ with the axis of symmetry of the parabola, then point of contact(s) is/are