Find the equation of the hyperbola in the cases given below: Foci (± 2, 0), Eccentricity = 32 - Mathematics

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

Foci (± 2, 0), Eccentricity = `3/2`

Sum

e = `3/2`

Foci (±c ,0) = (±2, 0)

c = 2

ae = 2

`a(3/2)` = 2

a = `4/3`, a² = `16/9`

b² = c² – a²

= `4 - 16/9`

= `20/9`

Equation of hyperbola

`x^2/"a"^2 - y^2/"b"^2` = 1

`x^2/(16/9) - y^2/(20/9)` = 1

`(9x^2)/16 - (9y^2)/20` = 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 3. (i) | Page 196

The parabola y² = kx passes through the point (4, -2). Find its latus rectum and focus.

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

y² = 20x

The profit ₹ y accumulated in thousand in x months is given by y = -x² + 10x – 15. Find the best time to end the project.

The double ordinate passing through the focus is:

The distance between directrix and focus of a parabola y² = 4ax is:

The equation of directrix of the parabola y² = -x is:

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

Focus (4, 0) and directrix x = – 4

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

y² = 16x

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

y² = – 8x

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

x² – 2x + 8y + 17 = 0