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

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

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

y² = 20x

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

x² = 8y

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

x² = - 16y

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

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

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

Focus (4, 0) and directrix x = – 4

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 parabola in the cases given below:

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