Question 12 Marks
Find the vertex, focus, axis, directrix and latus-rectum of the following parabolas:
y2 = 8x.
y2 = 8x.
Answer
View full question & answer→The given parabola y2 = 8x is of the form y2 = 4ax, where 4a = 8
$\Rightarrow\text{a}=\frac{8}{4}=2.$
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 = 4a = 4 × 2 = 8.
$\Rightarrow\text{a}=\frac{8}{4}=2.$
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 = 4a = 4 × 2 = 8.