Terminologies Related to a Parabola

Q.

The length of the latus rectum of the ellipse $5x^2+9y^2=45$ is

1. 

2. 

3. 

4. 

Q.

Find the coordinates of the foci, and the vertices, the eccentricity and the length of the latus rectum of the hyperbola,

$\frac{x^2}{16}-\frac{y^2}{9}=1$

Q.

The focal distance of a point on the parabola $y^2=8x$ is 10. Its coordinates are

1. (2, ±2)

2. (3, ±3)

3. (5, ±5)

4. (8, ±8)

Q. The point on the parabola $y^2=36x$ whose ordinate is three times its abscissa is

1. (4, 12)

2. (3, 9)

3. (6, 18)

4. (1, 3)

Q.

On the parabola $y=x^2$, the point least distance from the straight line$y=2x-4$ is

1. (1, 0)

2. (1, -1)

3. (0, 0)

4. (1, 1)

Q. The number of focal chords of length $\frac{4}{7}$ in the parabola $7y^2=8x$ is

1. zero
2. two
3. infinite
4. one

Q.

The two points A and B in a plane are such that for all points P lies on circle satisfied $\frac{PA}{PB}=k$, then k will not be

equal to

1. 3

2. 2

3. 0

4. 1

Q.

The Equation of the directrix to parabola $y^2=8x$ is _____

1. x + 2 = 0

2. x + 3 = 0

3. x = 0

4. x + 1 = 0

Q.

The locus of the midpoint of the line segment joining the focus to a moving point on the parabola $y^2=4ax$ is another parabola with the directrix

1. 

2. 

3. 

4. 

Q.

From a point on the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ lines are drawn to focus S

and directrix perpendicular to it as shown.Then,

1. 

2. 

3. 

4. 

Q.

Is a Parabola an Ellipse?

Q.

Consider a circle with its centre lying on the focus of the parabola $y^2=2px$ such that it touches the directrix
of the parabola. Then, a point of intersection of the circle and the parabola is

1. 

2. 

3. 

4. 

Q.

The focus of the parabols $x^2=-16y$ is

1. (4, 0)

2. (0, 4)

3. (-4, 0)

4. (0, -4)

Q.

The vertices of a triangle are $\mathrm{A}(-4,2),\mathrm{B}(-2,2)$ and $\mathrm{C}(-3,4)$. Rotate the triangle as described. Find the coordinates of the image.

$180°$ about the origin.

Q.

The co-ordinates of the extremities of the latus rectum of the parabola $5y^2=4x$ are

1. None of these

2. 

3. 

4. 

Q.

A chord BC is drawn in a parabola $y^2=4x$ such that x cordinate of C is twice that of B. Also OB makes ${45}^{\circ }$ with x-axis. What is the projecton of BC on y-axis?

___

Q. The ends of latus rectum of parabola $x^2+8y=0$ are

1. (-4, -2) and (4, -2)

2. (-4, -2) and (4, 2)

3. (4, -2) and (-4, 2)

4. (4, 2) and (-4, 2)

Q. Subtangent is theprojectionon to the x- axis of that part of atangentlying between its point of tangency with the curve and itsintersectionwith the x-axis.

1. True

2. False

Q.

The end points of latus rectum of the parabola $x^2=4ay$ are

1. 

2. 

3. 

4. 

Q.

Select the right options about a hyperbola.

1. Conjugate axis is the axis of the hyperbola that passes through the foci

2. A transverse axis always pass through the origin

3. The straight line through the centre which is perpendicular to the transverse axis doesn't meet hyperbola in real point.

4. Eccentricity is the ratio of 2 distances

Q.

The focus of the parabols $x^2=-16y$ is

1. (4, 0)

2. (0, 4)

3. (-4, 0)

4. (0, -4)

Q.

Match the following. Equation of the parabola is $y^2=4ax$

$\begin{array}{cc}\text{Column 1}& \text{Column 2}\\ \text{P) Focal distance}& \text{T) Focal chord perpendicular to axis}\\ \text{Q) Double ordinate}& \text{U) A chord perpendicular to axis}\\ \text{R) Latus rectum}& \text{V) Distance of a point on parabola from directrix}\\ \text{S) Vertex}& \text{W) Meeting point of axis and parabola}\end{array}$

1. P - V, Q - U, R - T, S - W

2. P - T, Q - U, R - V, S - W

3. P - V, Q - U, R - W, S - T

4. P - U, Q - V, R - T, S - W

Q.

Which of the following statements are correct?

1. The focus of $x^2=4ay$ is $(0,a)$

2. The directrix of $y^2=-4ax$ is $x+a=0$

3. The end points of latus rectum of $x^2=-4ay$ is (a, 2a) and (a, -2a)

4. The parabolas $x^2=4ay\text{and}{y}^2=4ax$ are equal.

Q. Find the coordinates of the focus axis of the parabola the equation of directrix and the length of the latus rectum for y${}^2=10x$

Q. Match the following for the parabola $y^2=4ax$:

1. Focal distance
2. Double ordinate
3. Latus rectum

Q. Find the coordinates of the focus, axis of the parabola , the equation of directrix and the length of the latus reactum for $x$ ${}^2=6y$