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Recent questions tagged sec-1

If the centre of the ellipes is $(4 , -2 ) $ and one of the focus is $(4 , 2 ),$ find the other focus?

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the vertices are $(\pm 4 , 0)$and $e=\large\frac{\sqrt{3}}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(\pm 3 , 0 ),$ and the length of the latus rectum is $\large\frac{32}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre is$ (3 , -1 ),$ one of the foci is $(6 , -1)$ and passing through the point $(8 , -1)$.

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the length of the semi major axis, and the latus rectum are $7$ and $\large\frac{80}{7}$ respectively, the centre is $(2 , 5 )$ and the major axis is parallel to y- axis.

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre at the origin, the major axis is along $x$-axies,$e=\large\frac{2}{3}$ and passes through the point $(2 , \large\frac{-5}{3})$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the centre is $(3 , -4 ), $one of the foci is $(3+\sqrt{3},-4)$ and $e=\large\frac{\sqrt{3}}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(\pm 3 , 0 )$ and the vertices are $(\pm 5 , 0)$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if the foci are $(2 , -1 ) , (0 , -1 )$ and $e=\large\frac{1}{2}$

asked Apr 10, 2013 by poojasapani_1

1 answer

Find the equation of the ellipse if One of the foci is$(0 , -1 )$, the corresponding directrix is $3x+16=0$ and $e=\large\frac{3}{5}$

asked Apr 10, 2013 by poojasapani_1

1 answer

A cable of a suspension bridge is in the form of a parabola whose span is $40mts$ . The road way is $5mts$ below the lowest point of the cable . if an extra support is provided across the cable $30mts$ above the ground level, Find the length of the support if the height of the pillars are $55mts$.

asked Apr 9, 2013 by poojasapani_1

1 answer

The focus of a parabolic mirror is at a distance of $8cm$ from its centre (vertex) ,if the mirror is $25cm$ deep, find the diameter of the mirror.

asked Apr 9, 2013 by poojasapani_1

1 answer

If a parabolic reflector is $20cm$ in diameter and $5cm$ deep, find the distance of the focus from the centre of the reflector.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $x^{2}-6x-12y-3=0$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}+8x-6y+1=0$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $(x-4)^{2}=4(y+2).$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs.$x^{2}=20y $

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the axies, vertex, focus, equation of directrix , latus rectum , length of the latus rectum for the following parabolas and hence sketch their graphs. $y^{2}=-8x$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(2 , 3 )$ open upward ;and passing through the point $(6 , 4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if :Vertex $(3 , -1 );$ open rightward ; the distance between the latus recturm and directrix is $4$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(3 , -2 ); $ open downward and the length of the latus rectum is $8$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 2 ) ;$ latus recturm :$y=5$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(1 , 4 );$ focus :$(-2 , 4 ).$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Vertex $(0 , 0 ); $ focus : $(0 , -4 )$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus: $(-1 , 3 )$; directrix $ 2x+3y=3$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the equation of parabola if : Focus:$(2 , -3 );$ directrix :$2y-3=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

Show that diameter of a sphere subtends a right angle at a point on the surface.

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres: $\overrightarrow{r}^{2}-\overrightarrow{r} . (\overrightarrow{4i}+\overrightarrow{2j}-\overrightarrow{6k})-11=0$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres :$x^{2}+y^{2}+z^{2}+4x-8x+2z=5$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres : $|\overrightarrow{2r}+(\overrightarrow{3i}-\overrightarrow{j}+\overrightarrow{4k})|=4$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the centre and radius of the following spheres : $| \overrightarrow{r}-(\overrightarrow(2i)-\overrightarrow(j)+\overrightarrow{4k})|=5$

asked Apr 9, 2013 by poojasapani_1

1 answer

If $A (-1 , 4 , -3 ) $ is one end of a diameter $AB$ of the sphere $ x^{2}+y^{2}+z^{2}-3x-2y+2z-15=0$ than, Find the coordinates of $B$.

asked Apr 9, 2013 by poojasapani_1

1 answer

Obtain the vector and cartesian equation of thesphere whose centre is $(1 , -1 , 1 )$ and radius is the same as that of the sphere $|\overrightarrow{r}-(\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{2k})|=5.$

asked Apr 9, 2013 by poojasapani_1

1 answer

Find the vector and cartesian equationof the sphere on the join of the points $A$ and $B$ having position vectors $\overrightarrow{2i}+\overrightarrow{6j}-\overrightarrow{7k}$ and $-\overrightarrow{2i}+\overrightarrow{4j}-\overrightarrow{3k}$ respectively as a diameter . Find also the centre and radius of the sphere.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the vector equation of a sphere with centre having position vector $\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{3k}$ and radius $4$ units. Also find the equation in cartesian form.

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between the line $\overrightarrow{r}=\overrightarrow{i}+\overrightarrow{j}+\overrightarrow{3k}+\lambda(\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{k})$ and the plane $\overrightarrow{r}.(\overrightarrow{i}+\overrightarrow{j})=1.$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between the line $\large\frac{x-2}{3}=\frac{y+1}{-1}=\frac{z-3}{-2}$and the plane $3x+4y+z+5=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

The planes $\overrightarrow{r} .(\overrightarrow{2i}+\lambda\overrightarrow{j}-\overrightarrow{3k})=10 $and $ \overrightarrow{r}. (\lambda\overrightarrow{i}+\overrightarrow{3j}+\overrightarrow{k})=5$ are perpendiculare find $\lambda$

asked Apr 8, 2013 by poojasapani_1

1 answer

Show that the following planes are at right angles.$\overrightarrow{r}(\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k})=15$ and$ \overrightarrow{r}(\overrightarrow{i}-\overrightarrow{j}-\overrightarrow{3k})=3$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following plane:$r=(3i+j-k)=7 $ and $r=(i+4j-2k)=10$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between following planes; $2x-3y+4z=1$ and $-x+y=4$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the angle between the followin planes: $2x+y-z=9 $and $x+2y+z=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the distane between the parallel planes $x-y+3z+5=0; 2x-2y+6z+7=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the distance from the origin to the plane $\overrightarrow{r}=(\overrightarrow{2i}+\overrightarrow{j}+\overrightarrow{5j})=7$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the meeting point of the line $\overrightarrow{r}(\overrightarrow{2i}+\overrightarrow{j}-\overrightarrow{3k}) + t(\overrightarrow{2i}-\overrightarrow{j}-\overrightarrow{k}) $ and the plane. $x-2y+3z+7=0$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the point of intersection of the line $\overrightarrow{r}=(\overrightarrow{j}-\overrightarrow{k})+s(\overrightarrow{2i}-\overrightarrow{j}+\overrightarrow{k})$ and $x z$ - plane.

asked Apr 8, 2013 by poojasapani_1

1 answer

Can u draw a plane through the given two lines? justify your answer.$\overrightarrow{r}(\overrightarrow{i}+\overrightarrow{2j}-\overrightarrow{4k})+t (\overrightarrow{2i}+\overrightarrow{3j} +\overrightarrow{6k})$ and $ r=(\overrightarrow{3i}+\overrightarrow{3j}-\overrightarrow{5k})+ s(-\overrightarrow{2i}+\overrightarrow{3j}+\overrightarrow{8k})$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the equations of the plane which contains the two lines $\large\frac{x+1}{2}=\frac{y-2}{-3}=\frac{z-3}{4}$ and $\large\frac{x-4}{3}=\frac{y-1}{2}=z-8$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the cartesian form of following planes: $\overrightarrow{r}=(1+s+t) \overrightarrow{i}+(2-s+t)\overrightarrow{j}+(3-2s+2t)\overrightarrow{k}$

asked Apr 8, 2013 by poojasapani_1

1 answer

Find the cartesian form of following planes:$ \overrightarrow{r}=(s-2t) \overrightarrow{i}+(3-t)\overrightarrow{j}+(2s+t)\overrightarrow{k}$

asked Apr 8, 2013 by poojasapani_1

1 answer

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