Four Common Forms of Parabola Equation

Q. Axis of the parabola $x^2-4x-3y+10=0$ is

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

Q. The focus of parabola $x^2=-16y$ is​

1. (4, 0)
2. (0, 4)
3. (-4, 0)
4. (0, -4)

Q. The equation of the parabola with its vertex at the origin, axis on the y-axis and passing through the point (6, -3) is

1. $y^2=12x+6$
2. $x^2=12y$
3. $x^2=-12y$
4. $y^2=-12x+6$

Q. Equation of the parabola whose vertex is $(-3,-2)$, axis is horizontal and which passes through the point $(1,2)$ is

1. $y^2+4y+4x-8=0$
2. $y^2+4y-4x+8=0$
3. $y^2+4y-4x-8=0$
4. none of these

Q. The equation of the latus rectum of the parabola $x^2+4x+2y=0$ is

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

Q. Vertex of the parabola $9x^2-6x+36y+9=0$ is

1. $(\frac{1}{3},\frac{-2}{9})$
   
2. $(\frac{-1}{3},\frac{-1}{2})$
   
3. $(\frac{-1}{3},\frac{1}{2})$
4. $(\frac{1}{3},\frac{1}{2})$

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

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. An equilateral triangle is inscribed in the parabola $y^2=4ax$ such that one vertex of this triangle coincides with the vertex of the parabola. The length of side of this triangle is

1. $2a\sqrt{3}$
2. $4a\sqrt{3}$
3. $6a\sqrt{3}$
4. $8a\sqrt{3}$

Q. The equation of the parabola whose axis is parallel to y – axis and passing through (4, 5), (–2, 11), (–4, 21) is

1. $x^2-4x-2y+10=0$
2. $x^2-2x-y+5=0$
3. $x^2-4x-2y+10=0$
4. $y^2-2x3y+4=0$

Q. The equation of the parabola whose vertex is (-1, -2) axis is vertical and which passes through the point (3, 6) is

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

Q. The equations $x=\frac{t}{4},y=\frac{t^2}{4}$ represents

1. A circle
2. A parabola
3. An ellipse
4. A hyperbola

Q. Equation of the parabola whose vertex is $(-3,-2)$, axis is horizontal and which passes through the point $(1,2)$ is

1. $y^2+4y+4x-8=0$
2. $y^2+4y-4x+8=0$
3. $y^2+4y-4x-8=0$
4. none of these

Q. For the given parabola $x^2+2y=8x-7$ which of the following is/are correct?

1. axis will be $2y=9$
2. axis will be $x=4$
3. vertex will be $(4,\frac{9}{2})$
4. vertex will be $(\frac{9}{2},4)$

Q. The equation of the parabola whose vertex is (-1, -2) axis is vertical and which passes through the point (3, 6) is

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

Q.

If we rotate $y^2=4ax$ by ${90}^{\circ }$ clockwise, we get $x^2=4ay$.

1. True

2. False

Q. Vertex of the parabola $9x^2-6x+36y+9=0$ is

1. $(\frac{1}{3},\frac{-2}{9})$
   
2. $(\frac{-1}{3},\frac{-1}{2})$
   
3. $(\frac{-1}{3},\frac{1}{2})$
4. $(\frac{1}{3},\frac{1}{2})$

Q. The equation of the latus rectum of the parabola $x^2+4x+2y=0$ is

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

Q. The equation of the parabola whose focus lies at the intersection point of the lines $x+y=3$ and $x-y=1$ and directrix is $x-y+5=0$

1. $x^2+y^2+2xy+18x+6y-25=0$
2. $x^2+y^2+2xy+18x+6y+25=0$
3. $x^2+y^2+2xy-18x+6y-15=0$
4. $x^2+y^2+2xy-18x-6y+15=0$

Q.

The vertex of a parabola is the point (a, b) and latus rectum is of length /. If the axis of the parabola is along the positive direction of y-axis, then its equation is

1. $(x+a{)}^2=\frac{l}{2}(2y-2b)$

2. $(x-a{)}^2=\frac{l}{2}(2y-2b)$

3. $(x+a{)}^2=\frac{l}{4}(2y-2b)$

4. $(x-a{)}^2=\frac{l}{8}(2y-2b)$