Recent questions in Conic Sections

Find the length of the line-segment joining the vertex of the parabola $y^2=4ax$ and a point on the parabola where the line-segment makes an angle $\theta$ to the $x$ -axis.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the coordinates of a point on the parabola $y^2 = 8x$ whose focal distance is 4.

asked Oct 10, 2014 by sreemathi.v

1 answer

Find the distance between the directrices of the ellipse $\large\frac{x^2}{36}+\frac{y^2}{20}$ $=1$ .

asked Oct 9, 2014 by sreemathi.v

1 answer

Find the equation of ellipse whose eccentricity is $\large\frac{2}{3}$ , latus rectum is 5 and the centre is (0, 0).

asked Oct 9, 2014 by sreemathi.v

1 answer

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

asked Oct 9, 2014 by sreemathi.v

1 answer

Given the ellipse with equation $9x^2+25y^2=225$ ,find the eccentricity and foci.

asked Oct 9, 2014 by sreemathi.v

1 answer

If the latus rectum of an ellipse is equal to half of minor axis,then find its eccentricity.

asked Oct 9, 2014 by sreemathi.v

1 answer

Find the equation of a circle concentric with the circle $x^2+y^2-6x+12y+15=0$ and has double of its area.

asked Oct 9, 2014 by sreemathi.v

1 answer

If the line $y=\sqrt 3x+k$ touches the circle $x^2+y^2=16$ ,then find the value of $k$ .

asked Oct 8, 2014 by sreemathi.v

1 answer

Find the equation of the circle having $(1,-2)$ as its centre and passing through $3x+y=14,2x+5y=18$ .

asked Oct 8, 2014 by sreemathi.v

1 answer

If one end of a diameter of the circle $x^2+y^2-4x-6y+11=0$ is $(3,4)$ ,then find the coordinate of the other end of the diameter.

asked Oct 8, 2014 by sreemathi.v

1 answer

Find the equation of a circle which touches both the axes and the line $3x-4y+8=0$ and lies in the third quadrant.

asked Oct 8, 2014 by sreemathi.v

1 answer

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

asked Jul 24, 2014 by thanvigandhi_1

1 answer

A man running a racecourse notes that the sum of the distances from the two flag posts from him is always 10 m and the distance between the flag posts is 8 m. Find the equation of the posts traced by the man.

asked Jul 24, 2014 by thanvigandhi_1

1 answer

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.

asked Jul 23, 2014 by thanvigandhi_1

1 answer

A rod of length 12 cm moves with its ends always touching the coordinate axes. Determine the equation of the locus of a point P on the rod, which is 3 cm from the end in contact with the x-axis.

asked Jul 23, 2014 by thanvigandhi_1

1 answer

An arch is in the form of a semi-ellipse. It is 8 m wide and 2 m high at the centre. Find the height of the arch at a point 1.5 m from one end.

asked Jul 23, 2014 by thanvigandhi_1

1 answer

The cable of a uniformly loaded suspension bridge hangs in the form of a parabola. The roadway which is horizontal and 100 m long is supported by vertical wires attached to the cable, the longest wire being 30 m and the shortest being 6 m. Find the length of a supporting wire attached to the roadway 18 m from the middle.

asked Jul 23, 2014 by thanvigandhi_1

1 answer

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?

asked Jul 23, 2014 by thanvigandhi_1

1 answer

If a parabolic reflector is 20 cm in diameter and 5 cm deep, find the focus.

asked Jul 23, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Foci $(0, \pm \sqrt{ 10} )$ , passing through $(2,3 )$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : vertices $(\pm 7,0 ) , e = \large\frac{4}{3}$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Foci $(\pm 4, 0)$ , the latus rectum is of length $12$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Foci $(\pm 3\sqrt 5 , 0)$ , the latus rectum is of length $8$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Foci $(0, \pm13)$ , the conjugate axis is of length $24$ .

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Foci $(\pm 5, 0)$ , the transverse axis is of length $8$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Vertices $(0, \pm 3),$ foci $(0, \pm 5)$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Vertices $(0, \pm 5),$ foci $(0, \pm 8)$

asked Jul 21, 2014 by thanvigandhi_1

1 answer

Find the equations of the hyperbola satisfying the given conditions : Vertices $(\pm 2, 0),$ foci $(\pm 3, 0)$

asked Jul 19, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $49y^2 – 16x^2 = 784$

asked Jul 19, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $5y^2-9x^2=36$

asked Jul 19, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $16x^2-9y^2=576$

asked Jul 19, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $9y^2–4x^2= 36$

asked Jul 19, 2014 by thanvigandhi_1

1 answer

Find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas : $\large\frac{y^2}{9}-\large\frac{x^2}{27}=1$

asked Jul 19, 2014 by thanvigandhi_1

1 answer