The equation of ellipse known in mathematics of senior two is x ^ 2 + 2Y ^ 2-4 = 0, then the equation of the straight line of the chord with m (1,1) as the midpoint is?

First, let the linear equation be Y-1 = K (x-1), then substitute it into the elliptic equation to get the quadratic equation of one variable about X or Y, and then X1 + x2 = 2 (midpoint), and then use the Veda theorem to solve it

It is known that the right focus of the hyperbola x24-y2b2 = 1 coincides with the focus of the parabola y2 = 12x. The distance from the focus of the hyperbola to its asymptote is obtained

∵ P = 6 of parabola y2 = 12x, opening direction to the right, ∵ focus is (3, 0), ∵ the right focus of hyperbola x24-y2b2 = 1 coincides with the focus of parabola y2 = 12x, ∵ 4 + B2 = 9, ∵ B2 = 5 ∵ the asymptote equation of hyperbola is y = ± 52X, that is, the distance from the focus of hyperbola to its asymptote is | 35 − 0 | 3 = 5

It is known that the left and right focus F1 and F2 of the ellipse x ^ 2 / (a ^ 2) + y ^ 2 / (a ^ 2-1) = 1 (a > 1), the parabola C: y ^ 2 = 2px, take F2 as the focus and intersect with the ellipse at points m (x1, Y1), n (X2, Y2), and the straight line f1m is tangent to the parabola C
(1) Find the equation of parabola C and the coordinates of points m and n
(2) Solving elliptic equation and eccentricity

(1) Ellipse x ^ 2 / (a ^ 2) + y ^ 2 / (a ^ 2-1) = 1 (a > 1)
Half focal length C = a ^ 2 - (a ^ 2-1) = 1
F1(-1,0),F2(1,0)
Parabola C: y ^ 2 = 2px, focusing on F2,
p/2=1,p=2,
y^2=4x
Straight line f1m: y = K (x + 1),
The line f1m is tangent to the parabola C,
That is, after the simultaneous equations, delt = 0
The equation is KY ^ 2-4y + 4K = 0
Delt = 0, k = 1 or K = - 1
Specify that M is above the x-axis
K = 1, y = 2, x = 1,
So m (1,2), n (1, - 2)
(2) M is on the ellipse, according to the definition of ellipse
MF1+MF2=2a
MF1^2=(1+1)^2+2^2=8
MF2^2=0^2+2^2=4
2a=2√2+2,a=√2+1
b^2=a^2-c^2=(√2+1)^2-1=2√2+2
Elliptic equation x ^ 2 / (3 + 2 √ 2) + y ^ 2 / (2 + 2 √ 2) = 1
e=c/a=1/(√2+1)=√2-1

Parabola y ^ 2 = 4x and ellipse x ^ 2 / 9 + y ^ 2 / k = 1 have common focus F1, F2 is another focus of ellipse, and P is an intersection of two curves,
Find (1) k value; (2) perimeter of △ pf1f2; (3) area of △ pf1f2

Parabola y ^ 2 = 4x and ellipse x ^ 2 / 9 + y ^ 2 / k = 1 have common focus F 1, F 2 is another focus of ellipse, P is an intersection of two curves
Find (1) k value; (2) perimeter of △ pf1f2; (3) area of △ pf1f2
Solution: (1) if the focus of the parabola is (1,0), then the two focuses of the ellipse should be on the x-axis, then K

The equation of ellipse known in mathematics of senior two is x ^ 2 + 2Y ^ 2-4 = 0, then the equation of the straight line of the chord with m (1,1) as the midpoint is?