# Find the co-ordinates of the focus, axis of the parabola, equations of the directrix and length of latus rectum of the parabola $y^2=12x$.

$\begin{array}{1 1}(3,0) \quad \text{ x-axis} \quad x+3 = 0 \quad 12 \\ (-3,0) \quad \text{ x-axis} \quad x-3 = 0 \quad 12 \\(3,0) \quad \text{ y-axis} \quad x-3 = 0 \quad 12 \\ (-3,0) \quad \text{ y-axis} \quad x+3 = 0 \quad 12\end{array}$

## 1 Answer

Toolbox:
Given $y^2 = 12x$
The co-efficient of $x$ is positive, comparing with $y^2 = 4ax \rightarrow 4a = 12 \rightarrow a = 3$
1) Therefore co-ordinates of the focus = $(a,0) = (3,0)$.
2) Since $y^2 = 12x$, the axis of the parabola is the x-axis
3) The Equation of the directrix $x = -a \rightarrow x = -3 \rightarrow x+3 = 0$
4) The Length of the Latus Rectum $= 4a = 4 \times 3 = 12$
answered Apr 1, 2014
edited Apr 1, 2014

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