Advertisements
Advertisements
प्रश्न
Find the equation of the ellipse with foci at (± 5, 0) and x = `36/5` as one of the directrices.
उत्तर
We have ae = 5, `a/e = 36/5`
Which give a 2 = 36 or a = 6
Therefore, e = `5/6`.
Now `b = asqrt(1 - "e"^2)`
= `6sqrt(1 - 25/36)`
= `sqrt(11)`.
Thus, the equation of the ellipse is `x^2/36 + y^2/11` = 1.
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^2/25 + 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.
36x2 + 4y2 = 144
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 parabolas
y2 − 4y − 3x + 1 = 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 = 8x + 8y
Find the vertex, focus, axis, directrix and latus-rectum of the following parabola
y2 = 5x − 4y − 9
For the parabola y2 = 4px find the extremities of a double ordinate of length 8 p. Prove that the lines from the vertex to its extremities are at right angles.
Write the axis of symmetry of the parabola y2 = x.
If the coordinates of the vertex and focus of a parabola are (−1, 1) and (2, 3) respectively, then write the equation of its directrix.
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
The vertex of the parabola (y − 2)2 = 16 (x − 1) 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:
3x2 + 4y2 − 12x − 8y + 4 = 0
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.
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.
Given the ellipse with equation 9x2 + 25y2 = 225, find the major and minor axes, eccentricity, foci and vertices.
The equation of the circle in the first quadrant touching each coordinate axis at a distance of one unit from the origin is ______.
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 ______.
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.
