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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 $y^2 = 10x$

$\begin{array}{1 1}(2.5,0) \quad \text{x-axis} \quad x = -2.5 \quad 10 \\ (-2.5,0) \quad \text{x-axis} \quad x = 2.5 \quad 10 \\ (-2.5,0) \quad \text{x-axis} \quad y = -2.5 \quad 10 \\ (2.5,0) \quad \text{y-axis} \quad y = -2.5 \quad 10 \end{array} $

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Given $y^2 = 10x$
The co-efficient of $x$ is positive, the parabola opens right. On comparing with $y^2=4ax \rightarrow 4a = 10 \rightarrow a = 2.5$
1) Therefore co-ordinates of the focus = $(a,0) = (2.5,0)$
2) Since $y^2=10x$, the axis of the parabola is the x-axis
3) The Equation of the directrix $ x = -a \rightarrow x = -2.5$
4) The Length of the Latus Rectum $ = 4a =4 \times 2.5 = 10$
answered Apr 1, 2014 by balaji.thirumalai
 

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