Current location - Training Enrollment Network - Mathematics courses - Mathematical model of grade nine in Haidian District II
Mathematical model of grade nine in Haidian District II
Solutions; As shown in the figure, the rectangular coordinate system is established.

According to the meaning of the question: Let the elliptic equation be X2A2+Y2B2 = 1 (a > b > 0).

(1) According to the meaning of the question: a2c=433, B = 1, A2 = B2+C2.

The eccentricity of ellipse M is greater than 0.7, so a2=4 and B2 = 1.

The elliptic equation is x24+y2 = 1.

(II) Because the straight line L passes through the origin and is at points p, q,

Let the left focus of ellipse m be f 1.

According to symmetry, quadrilateral PF 1QF2 is a parallelogram.

The area of ∴△PF2Q is equal to the area of △PF 1F2.

∫∠PF2Q = 2π3,

∴∠F 1PF2=π3.

Let |PF 1|=r 1, |PF2|=r2,

Then r 1+R2 = 4R2 1+R22? r 1r2= 12

∴r 1r2=43.

∴S△PF2Q=S△F2PF 1