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The distance between the foci of a hyperbola is 16 and its eccentricity is √2. Its equation is
The distance between the foci of a hyperbola is 16 and its eccentricity e = √2.
We know that The distance between the foci of a hyperbola = 2ae
⇒ 2ae = 16
⇒ α ∈ (–3, 0)
Hence option (2) is correct.
Calculation:
Enclosed Area
Concept:
If the function f(x) has an extremum at x = a then f'(a) = 0
Calculations:
xp + y (y(yp + z) + z(xp + y)) - (yp + z) (x(yp + z) - y(xp + y)) + 0(xz - y2) = 0
xp + y (y2p + yz - xzp - yz) - (yp + z) (xyp + xz - xyp - y2) = 0
(xp + y) (y2 p - xzp) - (yp + z) (xz - y2) = 0
(xp + y) p(y2 - xz) + (yp + z) (y2 - xz) = 0
(y2 - xz) ((xp + y)p + (yp + z)) = 0
(y2 - xz) (xp2 + yp + yp + z) = 0
(y2 = xz) (xp2 + 2yp + z) = 0
The determinant will be 0 if (y2 - xz) will be 0 which is geometric mean.
Hence x, y and z are in G.P.
CONCEPT:
The length x of a rectangle is decreasing at the rate of 5 cm/minute and the width y increasing at the rate of 4 cm/minute. If given that x = 0.06 meter and y = 0.02 meter than find the rate of change of area of the Rectangle?
Given that,
Let f(x + y) = f(x) f(y) and f(2) = 4 for all x, y ϵ R, where f(x) is continuous function. What is f' (2) equal to?
An unbiased coin is tossed 3 times, if the third toss gets head what is the probability of getting at least one more head?
Consider the following in respect of the function f(x) = |x - 3|:
1. f(x) is continuous at x = 3
2. f(x) is differentiable at x = 0.
Which of the above statements is / are correct?
LHD = RHD, so f(x) is differentiable at x = 0.
Hence, option (3) is correct.
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