It's very simple, but I can't do it 1. The straight line y = kx-2 and ellipse (x square) + 4 (y Square) = 80 intersect at two different points P and Q. if the abscissa of the midpoint of PQ is 2, then the chord length PQ is equal to_____ 2. P is the point on the ellipse (xsquare) / 12 + (ysquare) / 3 = 1, F1 and F2 are the two focal points. If the angle f1pf2 = 60 °, the area of the triangle f1pf2 is___

It's very simple, but I can't do it 1. The straight line y = kx-2 and ellipse (x square) + 4 (y Square) = 80 intersect at two different points P and Q. if the abscissa of the midpoint of PQ is 2, then the chord length PQ is equal to_____ 2. P is the point on the ellipse (xsquare) / 12 + (ysquare) / 3 = 1, F1 and F2 are the two focal points. If the angle f1pf2 = 60 °, the area of the triangle f1pf2 is___

1) Let P (x1, Y1), q (X2, Y2) then: X1 + x2 = 2 * 2 = 4, substituting y = kx-2 into x ^ 2 + 4Y ^ 2 = 80 to get: (1 + 4K ^ 2) x ^ 2-16kx-64 = 0x1 + x2 = 16K / (1 + 4K ^ 2), so 16K / (1 + 4K ^ 2) = 44K ^ 2 + 1-4k = 0k = 1 / 2 substituting (1 + 4K ^ 2) x ^ 2-16kx-64 = 0 to get: 2x ^ 2-8x-64 = 0x1 + x2 = 4, X1 = - 32 (x1-x

It is known that the straight line L: y = x + K passes through the right focus F2 of the ellipse C: x2a2 + y2a2-1 = 1, (a > 1) and intersects with the ellipse C at two points a and B. If a circle with the diameter of chord AB passes through the left focus F1 of the ellipse, the equation of the ellipse C is tried to be solved

Let the focal length of the ellipse be 2c, then C = a2 - (A2-1) = 1 (1) F2 (1, 0), substituting y = x + K & nbsp; & nbsp; to get k = - 1, substituting y = X-1 into elliptic equation to get: (2a2-1) x2-2a2x + 2a2-a4 = 0 Let a (x1, x1-1), B (X2, x2-1) ∵ AF1 ⊥ BF

Let F 1 and F 2 be the left and right focal points of the ellipse e: x ^ / A ^ + y ^ / b ^ = 1 (a > b > 0), the line L passing through F 1 with a slope of 1 intersects e at two points a and B, and the absolute values of AF 2, AB and BF 2 form an arithmetic sequence
(1) Find the eccentricity of e
(2) Let the point P (0, - 1) satisfy the absolute value of PA = the absolute value of Pb, and find the equation of E

A problem about ellipse in senior two,
A. B is the upper vertex and right vertex of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1, where a and B are two positive numbers. If P is a point on the first quadrant elliptic arc, what is the maximum area of △ ABP?