Given x + y = 10, find the value of [(x + y) ^ 2 - (X-Y) ^ 2-2y (X-Y)] / 5Y

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• 1. Square of (x + 2Y) (x-2y) - (2x-y) + (3x-y) (2x-5y) where x = - 1, y = 1 / 13
• 2. It is known that hyperbola m passes through point P (4, √ 6 / 2), and its asymptotic equation is x ± 2Y = 0
• 3. The hyperbolic equation which is asymptote with hyperbola 2x ^ 2-y ^ 2 = 2 and confocal with ellipse x ^ 2 + 2Y ^ 2 = 2 is?
• 4. Let f be a focal point of hyperbola C, p be an intersection of a parallel line passing through F as an imaginary axis and hyperbola, and Q be an intersection of a parallel line passing through F as an asymptote and hyperbola, Then PF / QF =?
• 5. [sharp!] hyperbola x ^ 2 / A ^ 2-y ^ 2-B ^ 2 = 1, if the inclination angle of an asymptote is 3 / π and the eccentricity is e, then the minimum value of (a ^ 2 + e) / b RT, the answer should be (2 √ 6) / 3, The problem is wrong, it should be x ^ 2 / A ^ 2-y ^ 2 / b ^ 2 = 1
• 6. The angle between two asymptotes of hyperbola x ^ 2-y ^ 2 / A ^ 2 = 1 (a > √ 2) is π / 3, and the eccentricity of hyperbola is calculated Say 2 √ 3 / 3?
• 7. Parallelogram ABCD, a (- 1,0), B (0, - 2) on the coordinate axis, ad = 5 and Y axis intersect at points e, C, D, two points on the hyperbola y = K / x, the area of quadrilateral BCDE Is 5 times the area of triangle Abe, then k =? Please Please help me
• 8. Taking the focus of the ellipse as the center of the circle and the focal length as the radius of the circle passing through the two vertices of the ellipse to calculate the eccentricity of the ellipse~- Taking the focus of the ellipse as the center of the circle and the focal length as the radius of the circle passing through the two vertices of the ellipse to calculate the eccentricity of the ellipse~ -In addition, do you need to consider which axis the ellipse is on
• 9. It is known that the hyperbola has a point P on one branch, the left and right focus is F1, F2, and | Pf1 | = 4 | PF2 |, so find the maximum value of eccentricity! Known hyperbola has a point P on a branch, the left and right focus is F1, F2, and | Pf1 | = 4 | PF2 |, find the maximum centrifugal rate, to complete the whole process of solving the problem!
• 10. F 1 and F 2 are the left and right focus of the hyperbola x ^ 2-y ^ 2 / 3 = 1, m (6,6) is a point inside the hyperbola, P is a point on the right branch of the hyperbola Find the minimum value of 〡 Pf1 〡 + 〡 PF2 〡
• 11. If x + 5Y = 6, then x2 + 5xy + 30y=______ ．
• 12. Find the center coordinate of the circle: X & # 178; + Y & # 178; - 2x + 4y-11 = 0, and the radius is
• 13. Find the following trajectory equation (1) for the center of circle m and circle C: (x + 2) &# 178; + Y & # 178; = 2, which is inscribed and passes through point a (2,0)
• 14. Given circle O: X & # 178; + Y & # 178; = 1 and point m (4,2) The equation for finding the straight line L through the tangent line L of the circle O in the direction of point m The equation for a circle m with chord length 4, which is cut by a straight line y = 2x-1 and centered on M Let p be any point in the middle circle m, passing through point P and leading tangent to circle O, and the tangent point is Q. try to explore whether there is a certain point R in the plane, so that PQ / PR is a fixed value? If there is, give an example. If not, explain the reason
• 15. The center F of the circle M: x = 1 + cos θ is a parabola e: x = 2pt & sup2; the focal point of the circle M: x = 1 + cos θ is a straight line intersection parabola e passing through the focal point F at two points y = sin θ y = 2pt Find the value range of afbf The center F of the circle M: x = 1 + cos θ y = sin θ is a parabola e: x = 2pt & sup2; the focal point of y = 2pt passes through the straight line intersection parabola e of the focal point F, and the value range of AF · BF is calculated at two points ab
• 16. If the center of the moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point------ Another problem: in the plane rectangular coordinate system xoy, two fixed points a and B on the parabola y2 = 4x which are different from the coordinate origin o are satisfied with AO vertical Bo, and the trajectory equation of the center of gravity g of the triangle AOB is obtained How to answer these two questions? How to find out?
• 17. The center is the origin, and the two focal points have a point P (3, t) on the ellipse on the x-axis. If the distance between the point P and the two focal points is 6.5 and 3.5 respectively, the elliptic equation is solved
• 18. Make a straight line L through point a (- 1,1) so that the midpoint of the line segment cut by two parallel lines L1: x + 2y-1 = 0 and: x + 2y-3 = 3 is exactly on the straight line L3: x-y-1 = 0, The equation for finding the line L
• 19. Given that two points a and B are on the line 2x-y = 0 and X + 2Y = 0 respectively, and the midpoint of AB segment is p (0,5), then the length of AB segment is______ ．
• 20. Make a straight line through the point m (0,1) so that the line segment cut by two straight lines L1: x-3y + 10 = 0, L2: 2x + Y-8 = 0 is exactly bisected by m, and solve the linear equation