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NTA Abhyas 2020

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

NTA Abhyas 2020 · Mathematics · Parabola

The coordinates of the focus of the parabola described...

The coordinates of the focus of the parabola described parametrically by

x = 5t^{2} + 2, y = 10t + 4

are

Options

A $(7,4)$
B $(3,4)$
C $( 3, - 4 )$
D $( - 7,4 )$

Correct answer

A. $(7,4)$

Step-by-step solution

Given parametric curves are

x = 5t^{2} + 2, y = 10t + 4

or

\dfrac{x - 2}{5} = t^{2}, \dfrac{y - 4}{10} = t

⇒ \dfrac{x - 2}{5} = { \left(\dfrac{y - 4}{10}\right)}

^{2}

<br /><br />

⇒

{ \left( y - 4\right)}

^{2} =

20\left(

x - 2\right)

<br /><br />

⇒ Y^{2} = 20X, whereY = y - 4, X = x - 2

<br /><br />

∴

Coodinate of focus is

( 5, 0 )

<br /><br />

ie

,

x - 2 = 5, y - 4 = 0

<br /><br />

⇒ x = 7, y = 4

<br /><br />Hence, the required coordinate is

( 7, 4 )

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