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Find the equation of the ellipse whose focus is (1, - 2), the directrix 3x – 2y + 5 = 0 and eccentricity equal to 1/2.
Find the equation of the ellipse in the following cases:
focus is (0, 1), directrix is x + y = 0 and .
focus is (- 1, 1), directrix is x - y + 3 = 0 and .
focus is (- 2, 3), directrix is 2x + 3y + 4 = 0 and
focus is (1, 2), directrix is 3x + 4y - 7 = 0 and .
Find the eccentricity, coordinates of foci, length of the latus - rectum of the following ellipse:
4x2 + 9y2 = 1
5x2 + 4y2 = 1
4x2 + 3y2 = 1
25x2 + 16y2 = 1600
9x2 + 25y2 = 225
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.
find the equation of the ellipse in the following cases:
eccentricity and foci (± 2, 0)
eccentricity and length of latus - rectum = 5
eccentricity and semi - major axis = 4
eccentricity and major axis = 12
The ellipse passes through (1, 4) and (- 6, 1)
Vertices (± 5, 0), foci (± 4, 0)
Vertices (0, ±13), foci (±4, 0)
Vertices (± 6, 0), foci (± 4, 0)
Ends of the major axis (± 3, 0), and of the minor axis (0, ±2)
Ends of the major axis (0, ± ), ends of the minor axis (±1,0)
Length of major axis 26, foci (±5, 0)
Length of minor axis 16 foci (0, ± 6)
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 the major axis is (i) parallel to x - axis (ii) parallel to the y - axis.
Find the eccentricity of an ellipse whose latus - rectum is
(i) Half of its minor axis
(ii) 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
x2 + 4y2 - 4x + 24y + 31 = 0
4x2 + y2 - 8x + 2y + 1 = 0
3x2 + 4y2 - 12x - 8y + 4 = 0
4x2 + 16y2 - 24x - 32y - 12 = 0
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 coordinates axes and which passes through (4, 3) and (- 1, 4).
Find the equation of an ellipse whose axes lie along the coordinates axes, which passes through the point (- 3, 1) and has eccentricity equal to .
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.
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 x - axis.
Find the equation of the set of all points whose distances from (0, 4) are of their distances from the line y = 9.
If the lengths of semi - major and semi - minor axes of an ellipse are 2 and √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 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 and B is an end of the minor axis such that Δ 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 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 as the end - points of a diameter is
The eccentricity of the ellipse 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 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
