How to calculate the distance from parabolic focus to hyperbolic asymptote?
The distance between the point and the line is | ax + by + C | / root sign (a ^ 2 + B ^ 2)
The hyperbola C and the ellipse have the same focus when the square of 8 / x plus the square of 4 / y equals 1. The asymptote of C is x with the straight line y equal to 3 times the root sign
Solving the equation of hyperbola C
Ellipse a ^ 2 = 8 B ^ 2 = 4
c^2=a^2-b^2=4
So the hyperbolic focus coordinates are (- 2,0) and (2,0)
Because the line y is equal to three times the root, X is an asymptote of C
Then B / a = √ 3
B = √ 3A square
b^2=3a^2
Hyperbola a a ^ 2 + B ^ 2 = C ^ 2 = 4
a=1 b=√3
The hyperbolic equation is x ^ 2-y ^ 2 / 3 = 1
In the following functions, the minimum value of 2 is a, y = 2 / x + X / 2 B, y = radical (x2 + 2) + 1 / radical (x2 + 2) C, y = 8 ^ x + 8 ^ (- x) d, y = x ^ 2 + 8 / X (x > 1)
According to the mean inequality, B and C can only be determined to be greater than 2, and there is no minimum value
A and D are not suitable for mean inequality
But it can be judged that the minimum value of item a is not 2
The answer can only be d
All formulas of arithmetic sequence (literal, including first term, last term, number of terms, general term and summation)
① Sum = (first item + last item) × number of items △ 2
(2) number of items = (last first item) △ tolerance + 1
(3) first term = 2 and △ number of terms - last term
(4) last term = 2 and △ number of terms - first term
(converted to the first inference of more than 2 terms)
(5) last item = first item + (number of items - 1) × tolerance