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Find the equation of the parabola that satisfies the given conditions: Vertex $(0,0)$ and Focus $(-2,0)$

$\begin{array}{1 1} y^2=-8x \\ x^2=-8y \\ x^2=-12y \\ x^2=12 y \end{array} $

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Given Vertex $(0,0)$ and Focus $(-2,0)$
Since the vertex is the origin and the focus lies on the positive x-axis, $\rightarrow $ x-axis is the axis of the parabola.
The parabola is of the form $y^2=-4ax$.
Since Focus = $(-3,0) \rightarrow a = 2$
Therefore the equation of the parabola is $y^2 =-4 \times 2x = -8x$
answered Apr 1, 2014 by balaji.thirumalai

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