Standard Equation of Parabola

Q. 12.Vertex (0, 0), passing through (5, 2) and symmetric with respect to y-axis.

Q. 9. Vertex (0, 0); focus (3, 0)

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 from the vertex of the parabola?

Q. 11. Vertex (0, 0) passing through (2, 3) and axis is alongx-axis.

Q. 7.Focus (6, 0); directrix x =-6

Q. 10. Vertex (0, 0); focus (-2, 0)

Q. Consider the two curves $C_1:y^2=4x,C_2:x^2+y^2-6x+1=0.$ Then,

1. $C_1$ and $C_2$ touch each other only at one point
2. $C_1$ and $C_2$ touch each other exactly at two points
3. $C_1$ and $C_2$ intersect (but do not touch) at exactly two points
4. $C_1$ and $C_2$ neither intersect nor touch each other

Q. The point P on the parabola $y^2=4ax$ for which $|PR-PQ|$ is maximum, where R = (-a, 0), Q = (0, a). is

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

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

1. (0, 0) (4, 12)
2. (1, 3), (4, 12)
3. (4, 12)
4. None of these

Q.

Find the equation of the ellipse whose foci are $(0,\pm 5)$ and the length of whose major axis is 20.

Q. An equilateral triangle is inscribed in the parabola y 2 = 4 ax , where one vertex is at the vertex of the parabola. Find the length of the side of the triangle.

Q. 212x

Q.

Find the equation of the hyperbola whose foci are at (0, $\pm 6)$ and the length of whose conjugate axis is $2\sqrt{11}$.

Q. Name the octants in which the following points lie:
$(1,2,3),(4,-2,3)(4,-2,-5),(4,2,-5),(-4,2,-5),(-4,2,5),(-3,-1,6),(2,-4,-7)$

Q. The number of point(s) (x, y) (where x and y both are perfect squares of integers) on the parabola $y^2=px$, p being a prime number, is

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

Q. 5, y2=1ox

Q. 3. y2--8x

Q. Find the coordinates of the focus, axis of the parabola, the equation of directrix and the length of the latus rectum for x 2 = –9 y

Q. Find the area of the triangle formed by the lines joining the vertex of the parabola $x^2=12y$ to the ends of its latus rectum.

Q.

The parabola $y^2=x$ is symmetric about

1. x – axis

2. y – axis

3. Both x – axis and y – axis

4. The line y = x

Q. The curve $y^2(a^2+x^2)=x^2(a^2-x^2)$ is symmetric about

1. $x-$axis
2. Origin
3. $y-$axis
4. straight line $x=y$

Q. 4. x2=-16v

Q. $M$ is the foot of perpendicular from a point $P$ on a parabola $y^2=4ax$ to its directrix and $SPM$ is an equilateral triangle, where $S$ is the focus of the parabola. Then the value of $\frac{SP}{a}$ is