Question 12 Marks
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
$y^2 = 8x.$
$y^2 = 8x.$
Answer
View full question & 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 $=4 a=4 \times 2=8$.
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 $=4 a=4 \times 2=8$.