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It is known that the half focal length of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is C, and the line L passes through the point Given that the half focal length of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 is C, the line L passes through points (a, 0), (0, b), and the distance from the origin to line L is (√ 3) C / 4, the Quasilinear equation and asymptote equation of hyperbola are solved
Hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1, real half axis is a, imaginary half axis is B, half focal length is C, a ^ 2 + B ^ 2 = C ^ 2, linear equation: - B / a = Y / (x-a), BX + ay AB = 0, distance from origin to straight line d = | 0 + 0-ab | / √ (a ^ 2 + B ^ 2) = AB / C, known d = √ 3C / 4, AB / C = √ 3C / 4, ab = √ 3C ^ 2 / 4, (1) B = √ (C ^ 2-A ^ 2), substituting
Let the half focal length of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 be c
Let the half focal length of the hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (b > a > 0) be C, the straight line L passes (a, 0), (0, b), the distance from the origin to the straight line is known to be root 3C / 4, and the eccentricity of the hyperbola is__
Straight line L is transformed into general formula BX + ay-ab = 0 by intercept formula X / A + Y / b = 1
Root 3C / 4 = AB / C (distance formula from point to line)
Both sides square 3C ^ 4 = 16A ^ 2 (C ^ 2-A ^ 2) at the same time
3C ^ 4-16a ^ 2C ^ 2 + 16A ^ 4 = 0 (cross multiplication)
C ^ 2 = 4A ^ 2 or 3C ^ 2 = 4A ^ 2 e ^ 2 = 4 or 4 / 3, but B ^ 2 > A ^ 2 C ^ 2-A ^ 2 > A ^ 2 e ^ 2 > 2
So e ^ 2 = 4, e = 2
It's too hard to fight
Let the half focus of hyperbola x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1 (b > a > 0) be c
When the straight line L passes (a, 0), (0, b), the distance from the origin to the straight line is known to be the root 3C / 4, and the eccentricity of the hyperbola is__
RELATED INFORMATIONS
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- 4. [2/xy/(1/x+1/y)2+(x2+y2)/(x2+2xy+y2)]*2x/(x-y)
- 5. Factorization factor: x2-2xy + y2-4=______ ．
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- 9. As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function As shown in the figure, the vertices a, D and C of oabc and ADEF are on the coordinate axis, the point F is on the line AB, and the points B and E are on the function y = 1 / X (x)
- 10. The coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively (4 / 4) the coordinates of points a, B and C are (3,0), (1, 3 under the root sign) and (0,1) respectively to find the area of the quadrilateral oabc
- 11. Is the focal length of hyperbola 2C or C
- 12. It is known that F1F2 is the focus of the ellipse x2 / A2 + Y2 / B2 = 1 (a > b > 0), the point P is on the ellipse, and the angle f1pf2 = 90 °, the intersection of the line segment Pf1 and the axis is Q, and O is the origin of the coordinate. If the area ratio of the triangle f1oq to the quadrilateral of2pq is 1:2, the eccentricity of the ellipse is 0
- 13. The two focal points of ellipse C: X * 2 / A * 2 + y * 2 / b * 2 = 1 (a > b > 0) are F1 and F2. The point P is on ellipse C, and Pf1 ⊥ F1F2, Pf1 = 4 / 3, PF2 = 14 / 3 (1) Solving elliptic c-equation (2) If the line L passes through the center m of the circle x * 2 + y * 2 + 4x-2y = 0, the intersection ellipse C lies at two points a and B, and a and B are symmetric with respect to point m, the equation of the line L is obtained
- 14. The focus of the ellipse x ^ 2 / 12 + y ^ 2 / 3 = 1 is F1, F2, and the point P is on the ellipse. If the midpoint of Pf1 is on the Y axis, then the ratio of Pf1 to PF2 is? Mathematical
- 15. Given that F1 and F2 are two focal points of the ellipse X & sup2 / 100 + Y & sup2 / 64 = 1, and P is a point on the ellipse, find the maximum value of Pf1 × PF2
- 16. If the sum of the distances from a point on the ellipse to two focal points (- 4,0), (4,0) is equal to 10, then the length of the minor axis of the ellipse is
- 17. It is known that the length of the minor axis of the ellipse e is 6, and the distance from the focus f to one end of the major axis is 9, then the eccentricity of the ellipse e is equal to () A. 35B. 45C. 513D. 1213
- 18. How to prove that the sum of distances between any point and two focal points of an elliptic equation is 2a by using the distance formula between two points? The elliptic equation is (x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1) No soy sauce!
- 19. Why is the shortest distance from the focus of the ellipse to the end of the minor axis?
- 20. How to find the shortest distance between focus and ellipse? How to judge which point on the ellipse has the shortest distance to the focus? How to find the shortest distance from the point to the focus?