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Home  >>  CBSE XI  >>  Math  >>  Conic Sections
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Find the co-ordinates of the focus, axis of the parabola, equations of the directrix and length of latus rectum of the parabola $y^2=-8x$

$\begin{array}{1 1}(-2,0) \quad \text{x-axis} \quad x = 2 \quad 8 \\ (2,0) \quad \text{y-axis} \quad x = 2 \quad 8 \\ (2,0) \quad \text{y-axis} \quad x = -2 \quad 8 \\ (-2,0) \quad \text{x-axis} \quad x = -2 \quad 8\end{array} $

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Given $y^2=-8x$
The co-efficient of $x$ is negative, The parabola opens to the left. $y^2=-8x \rightarrow -4a = -8 \rightarrow a = 2$
1) Therefore co-ordinates of the focus = $(-a,0) = (-2,0)$
2) Since $y^2=-8x$, the axis of the parabola is the x-axis
3) The Equation of the directrix $ x = +a \rightarrow x=2$
4) The Length of the Latus Rectum $ = 4a =4 \times 2 = 8$
answered Apr 1, 2014 by balaji.thirumalai
 

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