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NTA Abhyas 2020

Exam: NTA Abhyas
Year: 2020
Subject: Mathematics
Chapter: Parabola

NTA Abhyas 2020 · Mathematics · Parabola

The equation of the tangent to the parabola y^ 2 = 4x whose slope...

The equation of the tangent to the parabola

y^{2} = 4x

whose slope is positive and which also touches

x^{2} + y^{2} = \dfrac{1}{2}

is

Options

A $y = x + 1$
B $y = 2x + 1$
C $x + y = 2$
D $y = 4x + \dfrac{1}{2}$

Correct answer

A. $y = x + 1$

Step-by-step solution

Tangent to parabola is

y = mx + \dfrac{1}{m}

Tangent to circle is

y = mx \pm \dfrac{1}{\sqrt{2}}\sqrt{1 + m^{2}}

For common tangent

\dfrac{1}{m^{2}} = \dfrac{1}{2}\left(1 + m^{2}\right) ⇒ m^{4} + m^{2} - 2 = 0

⇒ m^{2} = 1 ⇒ m = 1

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