The equation of the circle passing through the four intersections of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 and Y ^ 2 / A ^ 2 + x ^ 2 / b ^ 2 = 1 (a > b > 0)

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• 1. It is known that the focus of the ellipse is on the x-axis, passing (2, root sign 3), and the eccentricity is root sign 3 / 2
• 2. To find the hyperbolic equation with the same focus as the ellipse X & # 178 / 16 + Y & # 178 / 8 = 1, the asymptotic equation is x ± √ 3Y = 0
• 3. If the hyperbola and ellipse 3x ^ 2 + 4Y ^ 2 = 48 are in common focus, and the real axis length is equal to 2, then the hyperbolic equation is?
• 4. It is known that the ellipse x ^ 2 / M-Y ^ 2 = 1 (M > 1) and hyperbola x ^ 2 / n-y ^ 2 = 1 (n > 0) with the same two foci F 1 and F 2, P is one of their foci, then It is known that the ellipse x ^ 2 / M-Y ^ 2 = 1 (M > 1) and hyperbola x ^ 2 / n-y ^ 2 = 1 (n > 0) with the same two foci F 1 and F 2, and P is one of their foci, then the shape of triangle pf1f 2 is
• 5. Ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) and hyperbola x ^ 2 / M-Y ^ 2 / N = 1 (m, n > 0) have common focus, F1, F2, P are their common points Ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) and hyperbola x ^ 2 / M-Y ^ 2 / N = 1 (m, n > 0) have common focus F1, F2 and P are their common points (1) Using B and N to express cos ∠ f1pf2 (2) Let s △ f1pf2 = f (B, n)
• 6. Let ellipse C and hyperbola d have the same focus F1 (- 4,0), F2 (4,0), and the length of the major axis of ellipse is twice the length of the real axis of hyperbola. Try to find the trajectory equation of the intersection of ellipse C and hyperbola D
• 7. Given that the absolute value of the distance difference between a point on the hyperbola and two focal points (- 2,0) and (2,0) is 2, then the hypohyperbolic equation is A 3 / 3 x ^ 2-y ^ 2 = 1 B x ^ 2-2 / 3 y ^ 2 C 3 / x ^ 2-y ^ 2 = - 1 D x ^ 2-3 of Y ^ 2 = - 1
• 8. Given that the square of hyperbola 2x - the square of 3Y = 18, what is the absolute value of the distance difference between a point and two focal points on the hyperbola, and what is the focal length? Answer the specific steps
• 9. The two focal coordinates of the hyperbola are (- 5,0) (5,0), and the absolute value of the distance difference between the two focal points on the hyperbola is 8
• 10. If the right focus of hyperbola x ^ 2 / 9-y ^ 2 / 16 = 1 is F1, point a (9,2), and point m is on the hyperbola, then the distance from the minimum value m of Ma + 3 / 5mf1 to F1 is greater than that from it to the right "The distance between M and F1 is greater than the distance between M and the right guide line, d = e = C / a = 5 / 3 d=3/5MF1 Ma + 3 / 5mf1 = ma + d > = m distance to right guide line = 9-9 / 5 = 36 / 5 " Why is Ma + d not directly equal to the abscissa of a: 9?
• 11. It is known that the parabola y = x * X-2 has four intersections with the ellipse y * y / 4 + X * x = 1. The equation of the circle with these four intersections is solved
• 12. It is known that there are four intersections between the parabola y = X-2 and the ellipse X / 4 + y = 1, and the four intersections are in a circle, then the equation of the circle is___ .】
• 13. It is known that the parabola y = x ^ 2-2 and the ellipse x ^ 2 / 4 + y ^ 2 = 1 have four intersections If the four points are in a circle, the equation of the circle is
• 14. Let a focus of the ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) coincide with the focus of the parabola C: y ^ 2 = 8x, the eccentricity e = 2 radical 5 / 5, the right focus f passing through the ellipse be a straight line L not coincident with the coordinate axis, intersecting the ellipse at two points a and B. let m (1,0), and (MA vector + MB vector) ⊥ AB vector, find the equation of the straight line L
• 15. How to solve sin3x-cos3x-sinx + cosx?
• 16. cos3x/2×cosx/2-sin3x/2×sinx/2
• 17. sin3x/sinx+cos3x/cosx
• 18. Let f (SiNx) = cos2x, then f (1 / 3) is equal to?
• 19. Given the vector a = (SiNx, 1), B = (cosx, 1), X ∈ R. (1) when x = π 4, find the coordinates of vector a + B; (2) if the function f (x) = | a + B | 2 + m is an odd function, find the value of real number M
• 20. Given the vector a = (SiNx, 2), B = (1, - cosx), and a is perpendicular to B, find the value of TaNx and Tan (x-card / 4)