Question 12 Marks

Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas: $y^2 = 8x.$

Answer

The given parabola $y^2=8 x$ is of the form $y^2=4 a x$, where $4 a=8 \Rightarrow a=\frac{8}{4}=2$. Vertex: The co-ordinates of the vertex are $(0,0)$. Focus: The Co-ordinate of the focos are $(2,0)$. Axis: The equation of the axis is $=0$. Directrix: The equation of the directrix is $x=-2$. Latus-rectum: The length of the latus-rectum $=4 a=4 \times 2=8$.

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