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Answer the following:
Find the equation of the hyperbola in the standard form if eccentricity is `3/2` and distance between foci is 12.
Concept: undefined >> undefined
Answer the following:
Find the equation of the hyperbola in the standard form if length of the conjugate axis is 3 and distance between the foci is 5.
Concept: undefined >> undefined
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Answer the following:
Find the equation of the tangent to the hyperbola 7x2 − 3y2 = 51 at (−3, −2)
Concept: undefined >> undefined
Answer the following:
Find the equation of the tangent to the hyperbola x = 3 secθ, y = 5 tanθ at θ = `pi/3`
Concept: undefined >> undefined
Answer the following:
Find the equation of the tangent to the hyperbola `x^2/25 − y^2/16` = 1 at P(30°)
Concept: undefined >> undefined
Answer the following:
Show that the line 2x − y = 4 touches the hyperbola 4x2 − 3y2 = 24. Find the point of contact
Concept: undefined >> undefined
Answer the following:
Find the equations of the tangents to the hyperbola 3x2 − y2 = 48 which are perpendicular to the line x + 2y − 7 = 0
Concept: undefined >> undefined
Answer the following:
Two tangents to the hyperbola `x^2/"a"^2 - y^2/"b"^2` = 1 make angles θ1, θ2, with the transverse axis. Find the locus of their point of intersection if tan θ1 + tan θ2 = k
Concept: undefined >> undefined
Find variance and S.D. for the following set of numbers:
7, 11, 2, 4, 9, 6, 3, 7, 11, 2, 5, 8, 3, 6, 8, 8, 2, 6
Concept: undefined >> undefined
Find variance and S.D. for the following set of numbers:
65, 77, 81, 98, 100, 80, 129
Concept: undefined >> undefined
Compute variance and standard deviation for the following data:
| X | 2 | 4 | 6 | 8 | 10 | 12 | 14 | 16 | 18 | 20 |
| F | 8 | 10 | 10 | 7 | 6 | 4 | 3 | 4 | 2 | 6 |
Concept: undefined >> undefined
Compute the variance and S.D.
| X | 31 | 32 | 33 | 34 | 35 | 36 | 37 |
| Frequency | 15 | 12 | 10 | 8 | 9 | 10 | 6 |
Concept: undefined >> undefined
Following data gives age of 100 students in a college. Calculate variance and S.D.
| Age (In years) | 16 | 17 | 18 | 19 | 20 | 21 |
| No. of Students | 20 | 7 | 11 | 17 | 30 | 15 |
Concept: undefined >> undefined
Find mean, variance and S.D. of the following data:
| Classes | 10 – 20 | 20 – 30 | 30 – 40 | 40 – 50 | 50 – 60 | 60 – 70 | 70 – 80 | 80 – 90 | 90 – 100 |
| Frequency | 7 | 14 | 6 | 13 | 9 | 15 | 11 | 10 | 15 |
Concept: undefined >> undefined
Find the variance and S.D. of the following frequency distribution which gives the distribution of 200 plants according to their height:
| Height (in cm) | 14 – 18 | 19 – 23 | 24 – 28 | 29 – 33 | 34 – 38 | 39 – 43 | 44 – 48 |
| No. of plants | 5 | 18 | 44 | 70 | 36 | 22 | 5 |
Concept: undefined >> undefined
The mean of 5 observations is 4.8 and the variance is 6.56. If three of the five observations are 1, 3 and 8, find the other two observations
Concept: undefined >> undefined
Select the correct option from the given alternatives :
The standard deviation of a distribution divided by the mean of the distribution and expressing in percentage is called:
Concept: undefined >> undefined
Select the correct option from the given alternatives :
If the S.D. of first n natural numbers is `sqrt(2)`, then the value of n must be ––––––.
Concept: undefined >> undefined
Select the correct option from the given alternatives :
The positive square root of the mean of the squares of the deviations of observations from their mean is called:
Concept: undefined >> undefined
Select the correct option from the given alternatives :
For any two numbers, SD is always
Concept: undefined >> undefined
