(A) The given equation is $y^{2}=8x$.Comparing this with the standard equation of a parabola $y^{2}=4ax$,we get $4a=8$,which implies $a=2$.Since the e

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Focus: $(2, 0)$,Axis: $y=0$,Directrix: $x=-2$,Latus Rectum: $8$

(A) The given equation is $y^{2}=8x$.Comparing this with the standard equation of a parabola $y^{2}=4ax$,we get $4a=8$,which implies $a=2$.Since the equation is of the form $y^{2}=4ax$,the axis of symmetry is the $x$-axis (i.e.,$y=0$).The focus of the parabola is $(a, 0) = (2, 0)$.The equation of the directrix is $x=-a$,which is $x=-2$.The length of the latus rectum is $4a = 4 \times 2 = 8$.

Class 11 Mathematics 10-2. Parabola, Ellipse, Hyperbola Parabola

Easy

Find the coordinates of the focus,axis,the equation of the directrix,and the length of the latus rectum of the parabola $y^{2}=8x$.

A
Focus: $(2, 0)$,Axis: $y=0$,Directrix: $x=-2$,Latus Rectum: $8$
B
Focus: $(0, 2)$,Axis: $x=0$,Directrix: $y=-2$,Latus Rectum: $8$
C
Focus: $(2, 0)$,Axis: $x=0$,Directrix: $x=2$,Latus Rectum: $4$
D
Focus: $(-2, 0)$,Axis: $y=0$,Directrix: $x=2$,Latus Rectum: $8$

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10-2. Parabola, Ellipse, Hyperbola

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Parabola

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

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If the line segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola makes an angle $\theta$ with the positive $X$-axis,then the length of that line segment is

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The equation of the parabola whose axis is vertical and passes through the points $(0, 0), (3, 0)$ and $(-1, 4)$ is

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Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y =-\frac{1}{2}$. Then $S=\left\{x \in R : \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}$:

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The point of contact of the tangent to the parabola $y^2 = 4ax$ which makes an angle of $60^\circ$ with the $x$-axis is:

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Find the coordinates of the focus,axis,the equation of the directrix,and the length of the latus rectum of the parabola $y^{2}=8x$.

Similar Questions

If the focus of a parabola is $(1, 0)$ and its directrix is $x + y = 5$,what is its vertex?

If the line segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola makes an angle $\theta$ with the positive $X$-axis,then the length of that line segment is

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Let $y=f(x)$ represent a parabola with focus $\left(-\frac{1}{2}, 0\right)$ and directrix $y =-\frac{1}{2}$. Then $S=\left\{x \in R : \tan ^{-1}\left(\sqrt{f(x)}+\sin ^{-1}(\sqrt{f(x)+1})\right)=\frac{\pi}{2}\right\}$:

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