Find the equation of the ellipse in the cases given below: Length of latus rectum 8, eccentricity = 35 centre (0, 0) and major axis on x -axis

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

Length of latus rectum 8, eccentricity = `3/5` centre (0, 0) and major axis on x-axis

Sum

e = `3/5`

Latus rectum `(2"b"^2)/"a"` = 8

b² = `"a"^2(1 -"e"^2)`

4a = `"a"^2 (1 - 9/25)`

4 = `"a"(16/25)`

⇒ `25/4` = a

a² = `625/16`

∴ b² = 4a

= `4(25/4)` = 25

∴ Equation of Ellipse `x^2/"a"^2 + y^2/"b"^2` = 1

⇒ `(16x^2)/625 + y^2/25` = 1

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Chapter 5: Two Dimensional Analytical Geometry-II - Exercise 5.2 [Page 196]

Chapter 5 Two Dimensional Analytical Geometry-II
Exercise 5.2 | Q 2. (iii) | Page 196

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

x² = - 16y

Find the equation of the parabola which is symmetrical about x-axis and passing through (–2, –3).

The focus of the parabola x² = 16y is:

The eccentricity of the parabola is:

The double ordinate passing through the focus is:

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

Passes through (2, – 3) and symmetric about y-axis

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

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

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

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