Double Ordinate

Q.

Find the equation of the hyperbola with centre at the origin, length of the transverse axis 6 and one focus at (0, 4).

Q.

The angle made by a double ordinate of length 8a at the vertex of the parabola $y^2=4ax$ is

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

2. $\frac{\pi }{2}$

3. $\frac{\pi }{4}$

4. $\frac{\pi }{6}$

Q. The parabola $y^2=4ax$ passes through the centre of the circle $4x^2+4y^2-8x+12y-7=0$. The directrix of the parabola will be

1. $4x+9=0$
2. $4x+15=0$
3. $16x+9=0$
4. $16x-7=0$

Q. If the locus of the circumcentre of of variable triangle having sides $y-$axis, $y=2$ and $lx+my=1$, where $(l,m)$ lies on the parabola $y^2=4ax$ is a curve $C$, then the curve $C$ is symmetric about the line

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

Q. Length of chord of contact of $(2,5)$ with respect to $y^2=8x$ is

1. $\frac{3\sqrt{41}}{2}$ units
2. $\frac{2\sqrt{17}}{3}$ units
3. $\frac{7\sqrt{3}}{5}$ units
4. $\frac{5\sqrt{3}}{7}$ units

Q. Let $y=f\left(x\right)$ be a parabola, having its axis parallel to $y-$axis, which is touched by the line $y=x$ at $x=1$, then

1. $f^{\prime }\left(0\right)=1-2f\left(0\right)$
2. $f\left(0\right)+f^{\prime }\left(0\right)+f^{\prime }\left(1\right)=1$
3. $f^{\prime }\left(1\right)=1$
4. $f^{\prime }\left(0\right)=f^{\prime }\left(1\right)$

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. Side length of this triangle is

1. $4a\sqrt{3}$

2. $6a\sqrt{3}$

3. $2a\sqrt{3}$

4. $8a\sqrt{3}$

Q. If $L_1$ and $L_2$ are the length of the segments of any focal chord of the parabola $y^2=x$, then $\frac{1}{L_1}+\frac{1}{L_2}$ is equal to

1. $2$
2. $3$
3. $4$
4. none of these

Q. Length of the latus rectum of the parabola $y=4x^2-4x+3$ will be

1. $\frac{1}{4}$ units
2. $2$ units
3. $\frac{3}{2}$ units
4. $4$ units

Q. If $p$ be the perpendicular distance of a focal chord $PQ$ of length $l$ from the vertex $A$ of the parabola $y^2=4ax$, then $l$ varies inversely as

1. $p^2$
2. $\frac{1}{p^2}$
3. $p$
4. $\frac{1}{p}$

Q. The locus of the point of intersection of tangents drawn at the extremities of a normal chord to the parabola $y^2=4ax$ is the curve

1. $y^2(x+2a)-4a^3=0$
2. $y^2(x+2a)+4a^3=0$
3. $y^2(x-2a)+4a^3=0$
4. $y^2(x-2a)-4a^3=0$

Q. The locus of points of trisection of double ordinate of $y^2=4ax$ is

1. $y^2=ax$
2. $9y^2=4ax$
3. $9y^2=ax$
4. $y^2=9ax$