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  • The equation of the parabola whose vertex and focus lie on the axis of x at distances   and

The equation of the parabola whose vertex and focus lie on the axis of x at distances \mathrm a  and \mathrm a_1  from the origin respectively is
 

Option: 1

\mathrm {y^2=4\left(a_1-a\right)(x)}


Option: 2

\mathrm {y^2=\left(a_1-a\right)(x-a)}


Option: 3

\mathrm {y^2=4 a_1 x}


Option: 4

\mathrm {y^2=4\left(a_1-a\right)(x-a)}


Answers (1)

best_answer


\begin{aligned} &\mathrm { A \text { is }(a, 0), S=\left(a_1, 0\right)} \\ & \mathrm {\therefore \quad A S=a_1-a=A }\\ & \mathrm {\therefore \quad \text { L.R. }=4 A S=4\left(a_1-a\right) }. \end{aligned}

Since the axis is the axis of x and vertex is the point  \mathrm {(a, 0)}  

hence by definition its equation is  \mathrm {Y^2=4 A X }

\mathrm {\: or\: (y-0)^2=4\left(a_1-a\right)(x-a) }

\mathrm {\: or \: y^2=4\left(a_1-a\right)(x-a). }

 

Posted by

Suraj Bhandari

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