RD Sharma solutions for Mathematics [English] Class 11 chapter 26 - Ellipse [Latest edition]

Find the equation of the ellipse in the case: 

 focus is (0, 1), directrix is x + y = 0 and e = \[\frac{1}{2}\] .

Find the equation of the ellipse in the case: 

 focus is (−1, 1), directrix is x − y + 3 = 0 and e = \[\frac{1}{2}\]

Find the equation of the ellipse in the case: 

focus is (−2, 3), directrix is 2x + 3y + 4 = 0 and e = \[\frac{4}{5}\]

Find the equation of the ellipse in the case: 

 focus is (1, 2), directrix is 3x + 4y − 5 = 0 and e = \[\frac{1}{2}\]

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:
 4x² + 9y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 5x² + 4y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 4x² + 3y² = 1

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

 25x² + 16y² = 1600.

Find the eccentricity, coordinates of foci, length of the latus-rectum of the ellipse:

Find the equation to the ellipse (referred to its axes as the axes of x and y respectively) which passes through the point (−3, 1) and has eccentricity \[\sqrt{\frac{2}{5}}\]

Find the equation of the ellipse in the case:

eccentricity e = \[\frac{1}{2}\] and foci (± 2, 0)

Find the equation of the ellipse in the case:

 eccentricity e = \[\frac{2}{3}\] and length of latus rectum = 5

Find the equation of the ellipse in the case: 

 eccentricity e = \[\frac{1}{2}\]  and semi-major axis = 4

Find the equation of the ellipse in the case:

eccentricity e = \[\frac{1}{2}\]  and major axis = 12

Find the equation of the ellipse in the case:

 The ellipse passes through (1, 4) and (−6, 1).

Find the equation of the ellipse in the case:

 Vertices (± 5, 0), foci (± 4, 0)

Find the equation of the ellipse in the case:

Vertices (0, ± 13), foci (0, ± 5)

Find the equation of the ellipse in the following case: 

Vertices (± 6, 0), foci (± 4, 0) 

Find the equation of the ellipse in the following case: 

Ends of major axis (± 3, 0), ends of minor axis (0, ± 2) 

Find the equation of the ellipse in the following case:  

Ends of major axis (0, ±\[\sqrt{5}\] ends of minor axis (± 1, 0) 

Find the equation of the ellipse in the following case: 

Length of major axis 26, foci (± 5, 0) 

Find the equation of the ellipse in the following case:  

Length of minor axis 16 foci (0, ± 6)

Find the equation of the ellipse in the following case:  

Foci (± 3, 0), a = 4

Find the equation of the ellipse whose foci are (4, 0) and (−4, 0), eccentricity = 1/3. 

Find the equation of the ellipse in the standard form whose minor axis is equal to the distance between foci and whose latus-rectum is 10. 

Find the equation of the ellipse whose centre is (−2, 3) and whose semi-axis are 3 and 2 when major axis is (i) parallel to x-axis (ii) parallel to y-axis.

Find the eccentricity of an ellipse whose latus rectum is  half of its minor axis  

Find the eccentricity of an ellipse whose latus rectum is  half of its major axis. 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

x² + 2y² − 2x + 12y + 10 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

 x² + 4y² − 4x + 24y + 31 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

4x² + y² − 8x + 2y + 1 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

3x² + 4y² − 12x − 8y + 4 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse: 

4x² + 16y² − 24x − 32y − 12 = 0 

Find the centre, the lengths of the axes, eccentricity, foci of the following ellipse:

x² + 4y² − 2x = 0 

Find the equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).

Find the equation of an ellipse whose eccentricity is 2/3, the latus-rectum is 5 and the centre is at the origin.

Find the equation of an ellipse with its foci on y-axis, eccentricity 3/4, centre at the origin and passing through (6, 4). 

Find the equation of an ellipse whose axes lie along coordinate axes and which passes through (4, 3) and (−1, 4). 

Find the equation of an ellipse whose axes lie along the coordinate axes, which passes through the point (−3, 1) and has eccentricity equal to \[\sqrt{2/5}\] 

Find the equation of an ellipse, the distance between the foci is 8 units and the distance between the directrices is 18 units.

Find the equation of an ellipse whose vertices are (0, ± 10) and eccentricity e = \[\frac{4}{5}\] 

A rod of length 12 m 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 x-axis. 

Find the equation of the set of all points whose distances from (0, 4) are\[\frac{2}{3}\] of their distances from the line y = 9. 

If the lengths of semi-major and semi-minor axes of an ellipse are 2 and \[\sqrt{3}\] and their corresponding equations are y − 5 = 0 and x + 3 = 0, then write the equation of the ellipse. 

Write the eccentricity of the ellipse 9x² + 5y² − 18x − 2y − 16 = 0. 

Write the centre and eccentricity of the ellipse 3x² + 4y² − 6x + 8y − 5 = 0. 

PSQ is a focal chord of the ellipse 4x² + 9y² = 36 such that SP = 4. If S' is the another focus, write the value of S'Q. 

Write the eccentricity of an ellipse whose latus-rectum is one half of the minor axis.

If the distance between the foci of an ellipse is equal to the length of the latus-rectum, write the eccentricity of the ellipse.

If S and S' are two foci of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] and B is an end of the minor axis such that ∆BSS' is equilateral, then write the eccentricity of the ellipse.

If the minor axis of an ellipse subtends an equilateral triangle with vertex at one end of major axis, then write the eccentricity of the ellipse. 

If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse. 

For the ellipse 12x² + 4y² + 24x − 16y + 25 = 0

The equation of the ellipse with focus (−1, 1), directrix x − y + 3 = 0 and eccentricity 1/2 is

The equation of the circle drawn with the two foci of \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] as the end-points of a diameter is

The eccentricity of the ellipse \[\frac{x^2}{a^2} + \frac{y^2}{b^2} = 1\] if its latus rectum is equal to one half of its minor axis, is

The eccentricity of the ellipse, if the distance between the foci is equal to the length of the latus-rectum, is

The eccentricity of the ellipse, if the minor axis is equal to the distance between the foci, is

The difference between the lengths of the major axis and the latus-rectum of an ellipse is

The eccentricity of the conic 9x² + 25y² = 225 is

The latus-rectum of the conic 3x² + 4y² − 6x + 8y − 5 = 0 is

The equations of the tangents to the ellipse 9x² + 16y² = 144 from the point (2, 3) are

The eccentricity of the ellipse 4x² + 9y² + 8x + 36y + 4 = 0 is

The eccentricity of the ellipse 4x² + 9y² = 36 is

The eccentricity of the ellipse 5x² + 9y² = 1 is

For the ellipse x² + 4y² = 9

If the latus rectum of an ellipse is one half of its minor axis, then its eccentricity is

An ellipse has its centre at (1, −1) and semi-major axis = 8 and it passes through the point (1, 3). The equation of the ellipse is

The sum of the focal distances of any point on the ellipse 9x² + 16y² = 144 is

If (2, 4) and (10, 10) are the ends of a latus-rectum of an ellipse with eccentricity 1/2, then the length of semi-major axis is

The equation \[\frac{x^2}{2 - \lambda} + \frac{y^2}{\lambda - 5} + 1 = 0\] represents an ellipse, if

The eccentricity of the ellipse 9x² + 25y² − 18x − 100y − 116 = 0, is

If the major axis of an ellipse is three times the minor axis, then its eccentricity is equal to

The eccentricity of the ellipse 25x² + 16y² = 400 is

The eccentricity of the ellipse 5x² + 9y² = 1 is

The eccentricity of the ellipse 4x² + 9y² = 36 is