Axis

Q.

If the eccentricity of an ellipse be $\frac{5}{8}$ and the distance between its foci be 10, then its latus rectum is

1. $\frac{39}{4}$

2. $12$

3. $15$

4. $\frac{37}{2}$

Q. If the normal to the rectangular hyperbola $xy=c^2$ at the point $(ct,\frac{c}{t})$ meets the curve again at $(c{t}^{\prime },{\frac{c}{t}}^{\prime }),$
then

1. 
2. 
3. 
4. 

Q. The area bounded by the parabola $y=4x^2,x=0$ and $y=1,y=4$ is equal to

1. $\frac{6}{3}$ Sq.units
2. $\frac{7}{3}$ Sq.units
3. $\frac{14}{3}$ Sq.units
4. $\frac{5}{3}$ Sq.units

Q.

If one of the lines of $m{y}^2+(1-m^2)xy-m{x}^2=0$ is a bisector of the angle between the lines $xy=0$, then $m$ is/are

1. $-\frac{1}{2}$

2. $-2$

3. $\pm 1$

4. $2$

Q. The length of the latus rectum of the hyperbola $9x^2-16y^2-72x-32y-16=0$ is

1. 
2. 
3. 
4. 

Q. The area of the region bounded by the curve $y=x-x^2$ and the line $y=mx$ equals $\frac{9}{2}\text{sq.units}$. Then the possible values of $m$ is/are:

1. $-4$
2. $-2$
3. $2$
4. $4$

Q. The area bounded between the parabolas $x^2=\frac{y}{4}$ and $x^2=9y$ and the straight line $y=2,$ is

1. $20\sqrt{2}$
2. $\frac{10\sqrt{2}}{3}$
3. $\frac{20\sqrt{2}}{3}$
4. $40\sqrt{2}$

Q.

The vertices of a triangle are J (-3, -5), K (-2, 2), and L (1, -4). Draw the figure and its reflection in:
(a) the x-axis and
(b) the y-axis.

Q. The focus of the conic $x^2-6x+4y+1=0$ is

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

Q. Find the equation of parabola if vertex $(0,0)$ passing through $(2,3)$ and axis is along $x-axis$.

Q. Find the equation of parabola vertex $(0,0)$, passing through $(5,2)$ and symmetric with respect to $y-axis$.

Q.

The axis of the parabola $9y^2-16x-12y-57-0$ is

1. 3y = 2

2. x + 3y =3

3. y = 3

4. 2x = 3

Q. Area of the region enclosed by the solutions of the inequality $(1.25{)}^{{\log }_3|z-1|}\le (0.64{)}^{{\log }_{1/9}2}\text{and}Re\left(Z\right)\le 0$ is

1. $(\frac{4\pi }{3}-\sqrt{3}){\text{unit}}^2$
2. $4\frac{\pi }{3}{\text{unit}}^2$
3. $\sqrt{3}{\text{unit}}^2$
4. $(\frac{4\pi }{3}+\sqrt{3}){\text{unit}}^2$

Q. The ends of the latus rectum of the conic $x^2+10x-16y+25=0$ are

1. (3, -4)
2. (-3, -4)
3. (3, 4), (-13, 4)
4. (5, -8), (-5, 8)

Q. The area enclosed between the curve $y={\log }_e(x+e)$ and the coordinate axes is

Q. For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$x^2=16y$

Q. If the vertex of the conic $y^2-4y=4x-4a$ always lies between the straight lines $x+y=3$ and $2x+2y-1=0$ then

1. $2<a<4$
2. $-\frac{1}{2}<a<2$
3. $-\frac{1}{2}<a<\frac{3}{2}$
4. $0<a<2$

Q. For the parabola $y^2=4x,$ the point $p$ whose focal distance is $17$ is

1. $(16,8)$ or $(16,-8)$
2. $(8,8)$ or $8,-8)$
3. $(4,8)$ or $(4,-8)$
4. None of these

Q. The vertex of the parabola $y=a{x}^2+bx+c$ is

1. $(\frac{b}{2a},\frac{b^2-4ac}{4a})$
2. $(\frac{-b}{2a},\frac{b^2-4ac}{4a})$
3. $(\frac{b}{2a},\frac{{4ac-b}^2}{4a})$
4. $(\frac{-b}{2a},\frac{{4ac-b}^2}{4a})$

Q. For the given parabola find the coordinates of focus, axis, the equation of the directrix and the length of the latus rectum.
$y^2=8x$

Q. Find the equation of parabola whose focus is $S(1,-7)$ and vertex is $A(1,-2)$.

Q. An equilateral triangle is inscribed in the parabola $y^2=4ax$ whose vertex is at the parabola. Find the length of its side.

1. $l=8a\sqrt{3}$
2. $l=8a\sqrt{2}$
3. $l=16a\sqrt{3}$
4. $l=4a\sqrt{3}$

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

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

Q. $A$: If $(9,12)$ is one end of a focal chord of the parabola $y^2=16x$ then the slope of it is
$B$: The parabola $x^2=py$ passes through $(12,16)$, the focal distance of the point is
$C$: If the parabola $y^2=kx$ passes through $(9,6)$ then the value of $k$ is
$D$: The Ordinate of the point on the parabola $y^2=36x$ whose ordinate is three times its abscissa is

1. $B,D,C,A$
2. $A,B,C,D$
3. $B,D,A,C$
4. $D,B,C,A$

Q. Find length of latus rectum of the parabola $y^2-2y=-2x-3$.

1. $2$
2. $-2$
3. $4$
4. $-4$

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

Q. Equation of tangent for the parabola $x^2=4ay$ is

1. $y=mx-a{m}^2$
2. $y=mx+a{m}^2$
3. $y=mx-\frac{a}{m}$
4. $y=mx+\frac{a}{m}$

Q. The area of the region $\text{(in sq.units)}$ formed by $x^2+y^2-6x-4y+12\le 0,y\le x$ and $x\le \frac{5}{2}$ is

1. $(\frac{1}{8}+\frac{\sqrt{3}}{8}-\frac{\pi }{6})$
2. $(\frac{1}{8}-\frac{\sqrt{3}}{8}+\frac{\pi }{6})$
3. $(\frac{1}{8}-\frac{\sqrt{3}}{8}-\frac{\pi }{6})$
4. None of these

Q. The function $f$ is defined by $f\left(x\right)=\left(x+3\right)\left(x+1\right)$.
The graph of $f$ in the $xy-plane$ is a parabola. Which of the following intervals contains the $x-coordinate$ of the vertex of the graph of $f$??

1. $-4<x<-3$
2. $-3<x<1$
3. $1<x<3$
4. $3<x<4$

Q. The equation of parabola whose focus is at $(4,-3)$ and the vertex is $(4,-1)$ is given by

1. $x^2-8x+8y+24=0$
2. $x^2-4x+8y+24=0$
3. $y^2-8y+8x+24=0$
4. $x^2-x+4y+20=0$