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 $y^2 = 8x$ is of the form $y^2 = 4ax,$ 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 $= 4a = 4 \times 2 = 8.$
$\Rightarrow\text{a}=\frac{8}{4}=2.$
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 $= 4a = 4 \times 2 = 8.$