Standard Form of a Hyperbola

Q.

Define double ordinate.

Q.

If the latus rectum of an hyperbola be 8 and eccentricity be $\frac{3}{\sqrt{5}}$ , then the equation of the hyperbola is

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Q.

From the prices of shares X and Y below, find out which is more stable in value :

$\begin{array}{ccccccccccc}X& 35& 54& 52& 53& 56& 58& 52& 50& 51& 49\\ Y& 108& 107& 105& 105& 106& 107& 104& 103& 104& 101\end{array}$

Q.

Find the equation of the hyperbola whose foci are $(\pm 5,0)$ and the transverse axis is of length 8.

Q.

The one which does not represent a hyperbola is

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Q.

Equation of the hyperbola with foci (0, ± 5) and e = $\frac{5}{3}$ is

1. $\frac{y^z}{9}-\frac{y^z}{16}=1$

2. $\frac{x^z}{12}-\frac{y^z}{13}=1$

3. $\frac{x^z}{16}-\frac{y^z}{9}=1$

4. $\frac{x^z}{16}-\frac{y^z}{9}=1$

Q.

A hyperbola passes through $(3,3)$ and the length of its conjugate axis is $8$. The length of the latus rectum is:

1. $\frac{20}{3}$

2. $\frac{40}{3}$

3. $\frac{50}{3}$

4. None of these

Q.

If the focal chord of the parabola $y^2=axis2x-y-8=0$, then the equation of directrix is.

1. x + 4 = 0

2. x - 4 = 0

3. y - 4 = 0

4. y + 4 = 0

Q. The locus of point of intersection of any tangent to the parabola $y^2=4a(x-2)$ with a line perpendicular to it and passing through the focus, is

1. y = 0
2. x = a
3. x = a + 2
4. x = 2

Q. Let ‘O’ be the centre of ellipse for which A, B are end points of major axis and C, D are end points of minor axis, F is focus of the ellipse. If in radius of $\Delta OCF$ is '1' then $|AB|\times |CD|=$

1. 65
2. 52
3. 78
4. 47

Q.

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

$16x^2-9y^2=576$

Q.

Find tha locus of the mid-point of the chords of the hyperbola $\frac{x^2}{2}-\frac{y^2}{3}=1$ which subtends a right angle at the origin

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Q. All chords of the curve ${3x}^2$-$y^2$-2x+4y = 0 that subtends a right angle at the origin, pass through a fixed point whose coordinates are

1. (-1, 2)
2. (-1, - 2)
3. (1, 2)
4. (1, −2)

Q. An arch is in the form of a parabola with its axis vertical. The arch is $10$ m high and $5$ m wide at the base. How wide is it $2$ m form the vertex of the parabola?

Q.

The length of the latus rectum and the length of the transverse axis of a hyperbola are $4\sqrt{3}\&2\sqrt{3}$ respectively, then the equation of the hyperbola can be

1. $\frac{x^2}{3}-\frac{y^2}{6}=1$

2. $\frac{x^2}{6}-\frac{y^2}{9}=1$

3. $\frac{x^2}{6}-\frac{y^2}{3}=1$

4. $\frac{x^2}{3}-\frac{y^2}{9}=1$

Q.

Find the equation of the hyperbola satisfying the given condition,

Foci $(\pm 5,0)$, the transverse axis is of length 8.

Q.

The length of the transverse axis of a hyperbola is 2cos t. The foci of the hyperbola are the same as that of the ellipse $9x^2+16y^2=144$.
The equation of the hyperbola is ___

1. $\frac{x^2}{co{s}^{2}t}-\frac{y^2}{7+co{s}^{2}t}=1$

2. $\frac{x^2}{1+co{s}^{2}t}-\frac{y^2}{7-co{s}^{2}t}=1$

3. $\frac{x^2}{co{s}^{2}t}-\frac{y^2}{7-co{s}^{2}t}=1$

4. $\frac{x^2}{1+co{s}^{2}t}-\frac{y^2}{7+co{s}^{2}t}=1$

Q. The equation to the hyperbola having its eccentricity equal to 2 and the distance between its foci equal to 8, is

1. x212-y24=1
2. x24-y212=1
3. x28-y22=1
4. x216-y29=1

Q. Find the equation of the hyperbola satisfying the given conditions: Foci $(\pm 3\sqrt{5},0)$ the latus rectum is of length $8$

Q.

What is the point of contact between the hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ and

in tangent $y=mx\pm \sqrt{a^2{m}^2-b^2}$.

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Q.

Length of the straight line $x-3y=1$ intercepted by the hyperbola $x^2-4y^2=1$ is

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Q.

If $(x_1,y_1)$ is a point inside the circle $x^2+y^2+2gx+2fy+c=0$ Given two expressions $S_1$ and $T_1$ such that,

$S_1=x_1^2+{y_1}^2+2g{x}_1+2f{y}_1+c$

$T_1=x{x}_1+y{y}_1+g(x+x_1)+f(y+y_1)+c$

Then the equation of chord centered at $(x_1,y_1)$ is

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Q.

Pair of straight lines perpendicular to each other represented by

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Q.

A standard hyperbola $\frac{x^2}{a^2}-\frac{y^2}{b^2}=1$ of eccentricity 'e' is given as below.

Choose the correct options.[S is the focus and dotted line is a directrix.]

1. \)

2. AB=2a

3. QS=me

4. SB=a(e-1)

Q.

If the eccentricity of a hyperbola is $\sqrt{2}$ and if the distance between the foci is 16, then its equation is

1. $x^2-y^2=4$

2. $x^2-y^2=8$

3. $x^2-y^2=16$

4. $x^2-y^2=32$

Q.

The equation to the hyperbola having its eccentricity 2 and the distance between its foci is 8, is,

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Q.

The equation to the hyperbola having its eccentricity equal to 2 and the distance between its foci equal to 8, is

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Q. A transverse axis of a hyperbola always passes through the origin.

1. True
2. False