Advertisements
Advertisements
प्रश्न
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is ______.
पर्याय
5x2 + 3y2 = 32
3x2 + 5y2 = 32
5x2 – 3y2 = 32
3x2 + 5y2 + 32 = 0
उत्तर
The equation of the ellipse whose centre is at the origin and the x-axis, the major axis, which passes through the points (–3, 1) and (2, –2) is 3x2 + 5y2 = 32.
Explanation:
Let `x^2/a^2 + y^2/b^2` = 1 be the equation of the ellipse.
Then according to the given conditions
We have `9/a^2 + 1/b^2` = 1 and `1/a^2 + 1/b^2 - 1/4`
Which gives `a^2 = 32/3` and `b^2 = 32/5`.
Hence, required equation of ellipse is 3x2 + 5y2 = 32.
APPEARS IN
संबंधित प्रश्न
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/4 + y^2/25 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/16 + y^2/9 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/25 + y^2/100 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
`x^2/49 + y^2/36 = 1`
Find the coordinates of the foci, the vertices, the length of major axis, the minor axis, the eccentricity and the length of the latus rectum of the ellipse.
4x2 + 9y2 = 36
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.
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola:
y2 = 8x
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
4x2 + y = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 + 4x + 4y − 3 = 0
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 8x + 8y
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 5x − 4y − 9
Write the distance between the vertex and focus of the parabola y2 + 6y + 2x + 5 = 0.
In the parabola y2 = 4ax, the length of the chord passing through the vertex and inclined to the axis at π/4 is
The equation of the parabola with focus (0, 0) and directrix x + y = 4 is
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:
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 equation of an ellipse whose foci are at (± 3, 0) and which passes through (4, 1).
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.
If a latus rectum of an ellipse subtends a right angle at the centre of the ellipse, then write the eccentricity of the ellipse.
Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.
The equation of the circle which passes through the point (4, 5) and has its centre at (2, 2) is ______.
If the lines 3x – 4y + 4 = 0 and 6x – 8y – 7 = 0 are tangents to a circle, then find the radius of the circle.
Find the distance between the directrices of the ellipse `x^2/36 + y^2/20` = 1
