Vertices of Hyperbola

Q. The equation of the hyperbola with vertices (3, 0), (–3, 0) and semi-latus rectum 4, is given by

1. 
2. 
3. 
4. None of these

Q.

The vertices of a hyperbola are (2, 0), (–2, 0) and the foci are (3, 0), (–3, 0). The equation of the hyperbola is

1. 

2. 

3. 

4. 

Q.

If the straight lines 2x+3y-1=0, x+2y-1=0and ax+by-1=0 forms a triangle with origin as orthocenter then (a, b) is

Q. The equation of the hyperbola with vertices (3, 0), (–3, 0) and semi-latus rectum 4, is given by

1. $4x^2-3y^2+36=0$
2. $4x^2-3y^2+12=0$
3. $4x^2-3y^2-36=0$
4. None of these

Q. STATEMENT-1: The locus of the centre of a circle which touches two given circles with different radius and centre will be a hyperbola.
and
STATEMENT-2: If the differnece of distance of a variable point to two given is always constant and less than the distnace between the points then the locus will be a hyperbola

1. Statement -1 is True, Statement-2 is True; Statement-2 is NOT a correct expalanation for Statement-1
2. Statement-1 is True, Statement-2 is False
3. Statement -1 is True, Statement-2 is True; Statement-2 is a correct expalanation for Statement-1
4. Statement-1 is False, Statement-2 is True.

Q. Show that the following points are coplanar.
(i) (0, −1, 0), (2, 1, −1), (1, 1, 1) and (3, 3, 0)
(ii) (0, 4, 3), (−1, −5, −3), (−2, −2, 1) and (1, 1, −1)

Q. The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are

1. and
2. and
3. and
4. None of these

Q. Vertex of the parabola $x^2+12x-9y=0$ is

1. $(6,-4)$
2. $(6,4)$
3. $(-6,-4)$
4. $(-6,4)$

Q. The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are:

1. (6, 3)
2. (-6, 3)
3. (2, 3)
4. (-2, 3)

Q. The vertex of the parabola $y^2+6x-2y+13=0$ is

1. $(1,-1)$
2. $(-2,1)$
3. $(\frac{3}{2},1)$
4. $(-\frac{7}{2},1)$

Q. Show that the four points (0, −1, −1), (4, 5, 1), (3, 9, 4) and (−4, 4, 4) are coplanar and find the equation of the common plane.

Q. Show that the following points are coplanar.
(i) (0, −1, 0), (2, 1, −1), (1, 1, 1) and (3, 3, 0)
(ii) (0, 4, 3), (−1, −5, −3), (−2, −2, 1) and (1, 1, −1)

Q. The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are:

1. (6, 3)
2. (-6, 3)
3. (2, 3)
4. (-2, 3)

Q. Determine the points in (i) xy-plane (ii) yz-plane and (iii) zx-plane which are equidistant from the points A(1, –1, 0), B(2, 1, 2) and C(3, 2, –1).

Q. The equation of the hyperbola with vertices (3, 0), (–3, 0) and semi-latus rectum 4, is given by

1. $4x^2-3y^2+36=0$
2. $4x^2-3y^2+12=0$
3. $4x^2-3y^2-36=0$
4. None of these

Q. Equation of the parabola whose vertex is $(0,0)$ and focus is the point of intersection of the lines $x+y=2,2x-y=4$ is

1. $y^2=4x$
2. $y^2=2x$
3. $x^2=8y$
4. $y^2=8x$

Q. The vertices of the hyperbola $9x^2-16y^2-36x+96y-252=0$ are:

1. (6, 3)
2. (-6, 3)
3. (2, 3)
4. (-2, 3)

Q. Q.17. Find the value of a for which the curve $y=x^2+ax+25$ touches the x-axis.