Find the equation of the ellipse in the cases given below: Foci (0, ±4) and end points of major axis are (0, ±5) - Mathematics

Find the equation of the ellipse in the cases given below:

Foci (0, ±4) and end points of major axis are (0, ±5)

बेरीज

Foci (0, ±c) = (0, +4)

Vertex (0, ±a) = (0, ±5)

∴ c = 4, a = 5

ae = 4

5e = 4

e = `4/5`

b² = a² – c²

= 25 – 16

b² = 9

Equation of the ellipse be `x^2/"b"^2 + y^2/"a"^2` = 1

`x^2/9 + y^2/25` = 1

shaalaa.com

या प्रश्नात किंवा उत्तरात काही त्रुटी आहे का?

पाठ 5: Two Dimensional Analytical Geometry-II - Exercise 5.2 [पृष्ठ १९६]

पाठ 5 Two Dimensional Analytical Geometry-II
Exercise 5.2 | Q 2. (ii) | पृष्ठ १९६

Find the equation of the parabola whose focus is the point F(-1, -2) and the directrix is the line 4x – 3y + 2 = 0.

Find the co-ordinates of the focus, vertex, equation of the directrix, axis and the length of latus rectum of the parabola

x² = 8y

The eccentricity of the parabola is:

The double ordinate passing through the focus is:

Find the equation of the hyperbola in the cases given below:

Foci (± 2, 0), Eccentricity = `3/2`

Find the equation of the hyperbola in the cases given below:

Passing through (5, – 2) and length of the transverse axis along x-axis and of length 8 units

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

x² = 24y

Find the vertex, focus, equation of directrix and length of the latus rectum of the following:

y² = – 8x