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

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

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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 axis, vertex, focus, equation of directrix and the length of latus rectum of the parabola (y - 2)² = 4(x - 1)

The double ordinate passing through the focus is:

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

End points of latus rectum (4, – 8) and (4, 8)

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

Foci `(+- 3, 0), "e"+ 1/2`

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

Length of latus rectum 4, distance between foci `4sqrt(2)`, centre (0, 0) and major axis as y-axis

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:

Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4