Taking the right focus of the hyperbola x square / 9-y square / 16 = 1 as the center of the circle, and the equation of the circle tangent to the two asymptotes is

a²=9
b²=16
c²=9+16=25
Right focus (5,0)
Asymptote y = (± B / a) x = (± 4 / 3) x
That is 4x ± 3Y = 0
Radius is the distance from right focus to asymptote = | 20 ± 0 | / √ (4 & sup2; + 3 & sup2;) = 4
So (X-5) & sup2; + Y & sup2; = 16

Given that the real axis of hyperbola is 4 and the root sign is 5, the focus is on the Y axis and passes through point a (2, - 5), then the standard equation of hyperbola is?

Let the equation be y ^ 2 / A ^ 2-x ^ 2 / b ^ 2 = 1
A = (4 radical 5) / 2 = 2 radical 5
That is y ^ 2 / 20-x ^ 2 / b ^ 2 = 1
Substituting a (2, - 5): 25 / 20-4 / b ^ 2 = 1
B ^ 2 = 16
The equation is y ^ 2 / 20-x ^ 2 / 16 = 1

RELATED INFORMATIONS

1. The focal points F1 (- 5,0) and F2 (5,0) of hyperbola C are known, and the length of major axis is 6 (1) Let the line y = x + 2 intersect the hyperbola C at two points a and B, and find the midpoint coordinates of line ab. (2) if the line y = KX + 2 has an intersection with the hyperbola, find the value range of K. (3) if the line y = KX + 2 has two intersections with a branch of the hyperbola, and the intersection points are a and B respectively, find the value range of K
2. The ellipse X & # 178 / M + Y & # 178 / M-1 = 1 (M > 1) intersects with the straight line y = X-1 at two points a and B. If AB is the left focus F of the ellipse, the value of the real number m is obtained,
3. What does the sign of the product determine in the multiplication of rational numbers‘
4. If the product of two rational numbers is positive, then the sign of the two factors must be positive______ ．
5. In high school mathematics, R is all real numbers. What is the scope of a
6. How to use English quantifiers It's like the meaning of description is also one, why do we have to use it? Please also talk about what other quantifiers should be used in where, please give an example It's like saying "bread" and "sheet slice" are the same. Why do you have to use "load"?
7. English quantifiers For various quantifiers, to plural For example, a school of fish The more like this, the better
8. English quantifier usage about glasses, baskets, six bowls of rice, five cups of tea, a cup of tea, a pair of glasses, ten pairs of eyes! And a glass of water, glasses or glass
9. Fill in quantifiers and word explanations 1. Fill in quantifiers A pair of golden hair A small sour fruit A little snowflake Think about it Clear spring like a silver arrow A solitary lamp two (1) Turn a deaf ear (2) Indifferent (3) Turn a blind eye (4) To the letter I've got a wrong number for "ring"
10. Zhang word group words, but quantifiers
11. If the distance between a point m on hyperbola x24-y212 = 1 and its right focus is 3, then the abscissa of point m is___ ．
12. The equation MX2 + 2 (M + 3) x + 2m + 14 = 0 of X has two real roots, one of which is greater than 4 and the other is less than 4
13. Given two real roots of the equation x2 + 2px + 1 = 0 about X, one is less than 1 and the other is greater than 1, then the value range of real number P is______ ．
14. Let m be an integer and - 4 < m is less than 1. The equation x & # 178; - 2 (2m-3) x + 4m & # 178; - 14m + 8 = 0 has two unequal real roots Finding the value of M and the solution of the equation
15. If the square root of (x + 2) is positive or negative 2, then the arithmetic square root of 2x + 5 is?
16. Square of 2002 + square of 2002 * square of 2003 + square of 2003 = a, it is proved that a is the complete square root
17. X + 3 / 4x = 5 / 8
18. Calculate or simplify (1) 12xy / 5A ／ 8x ^ 2Y (2) 1 - X-Y / x + 2Y ／ x ^ 2-y ^ 2 / x ^ 2 + 4xy + 4Y ^ 2 Calculation or simplification (1)12xy/5a÷8x^2y (2)1- x-y/x+2y÷x^2-y^2/x^2+4xy+4y^2 (3)(-ax^4y^3)÷(5/6ax^2y^2)= (4)(-2a^3b^2)^3÷(-3ab^3)^2= (5)3a/5xy=( )/10axy (a≠0) (6)a+2/a^2-4=1/( )
19. If the square of 4x + 4xy + 2Y = Y-1 / 4, find 2x + 4Y
20. How to solve the equation 11x + 33-3x = 96?