Definition of a Parabola

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.

If the parabola $y^2=4ax$ passes through (-3, 2), then length of its latus rectum is

1. 4

2. 2/3

3. 1/3

4. 4/3

Q.

Find the equation of the hyperbola, the length of whose latus rectum is $4$ and the eccentricity is $3$.

Q. If $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a parabola, then $abc+2fgh-a{f}^2-b{g}^2-c{h}^2$ is and

1. $h^2>ab$
2. $h^2<ab$
3. $h^2=ab$
4. not equal to 0
5. equal to 0

Q.

If the pair of straight lines given by $A{x}^2+2Hxy+B{y}^2=0,(H^2>AB)$ forms an equilateral triangle with line ax + by + c = 0, then (A + 3B)(3A + B) is

1. 

2. 

3. 

4. 

Q.

How many of the following statements are correct ___

1. A conic with eccentricity equal to one is called a parabola

2. If $a{x}^2+2hxy+b{y}^2+2gx+2fy+c=0$ represents a parabola, then

$abc+2fgh-a{f}^2-b{g}^2-c{h}^2\ne 0and{h}^2=ab$