(B) Given the parametric equations: $x = \frac{t}{4} \Rightarrow t = 4x$ Substitute $t = 4x$ into the equation for $y$: $y = \frac{(4x)^2}{4} = \frac{

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(B) Given the parametric equations: $x = \frac{t}{4} \Rightarrow t = 4x$ Substitute $t = 4x$ into the equation for $y$: $y = \frac{(4x)^2}{4} = \frac{16x^2}{4} = 4x^2$ Rearranging gives $x^2 = \frac{1}{4}y$,which is of the form $x^2 = 4ay$ (where $a = \frac{1}{16}$),representing a parabola.

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

Easy

The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

A
$A$ circle
B
$A$ parabola
C
An ellipse
D
$A$ hyperbola

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Class 11

Mathematics Questions

Chapter

10-2. Parabola, Ellipse, Hyperbola

Subtopic

Parabola

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

Medium

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If the focus of the parabola is $(3, -4)$ and the directrix is $y - 4 = 0,$ then the equation of the parabola is :-

Difficult

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The line $y = 2x + c$ is a tangent to the parabola $y^2 = 16x$,if $c$ equals

Easy

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The length of the latus rectum of the parabola $9x^2 + 16y^2 + 24xy - 4x + 3y = 0$ is

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If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

MediumTS EAMCET 2006

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The equations $x = \frac{t}{4}$ and $y = \frac{t^2}{4}$ represent:

Similar Questions

If the line $x + y = k$ is a normal to the parabola $y^2 = 4x$,find the value of $k$.

If the focus of the parabola is $(3, -4)$ and the directrix is $y - 4 = 0,$ then the equation of the parabola is :-

The line $y = 2x + c$ is a tangent to the parabola $y^2 = 16x$,if $c$ equals

The length of the latus rectum of the parabola $9x^2 + 16y^2 + 24xy - 4x + 3y = 0$ is

If $b$ and $c$ are the lengths of the segments of any focal chord of a parabola $y^2 = 4ax$,then the length of the semi-latus rectum is:

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