(2011 · Anhui simulation) the area of △ pf1f2 is () A. 20B. 22C. 24D. 28

(2011 · Anhui simulation) the area of △ pf1f2 is () A. 20B. 22C. 24D. 28

From the meaning of the title, we can get a = 7, B = 26, C = 5, two focuses F1 (- 5, 0), F2 (5, 0), and point P (m, n), then we can get & nbsp; nm + 5 · nm − 5 = - 1, M249 + n224 = 1, N2 = 24225, n = ± 245, then the area of △ pf1f2 is & nbsp; 12 × 2C ×| n | = 12 × 10 × 245 = 24, so we choose C

Let the equations of curves C1 and C2 be F1 (x, y) = 0 and F2 (x, y) = 0 respectively, then a sufficient condition that point P (a, b) does not belong to C1 ∩ C2 is?
For example, ask for detailed analysis and correct answer orz

F1 (a, b) + F2 (a, b) ≠ 0
Well, there are many sufficient conditions n. as long as (a, b) does not satisfy both F1 (a, b) = 0 and F2 (a, b) = 0

Circle system equation passing through the intersection of two circles C1: x ^ 2 + y ^ 2 + D1X + b1y + F1 = 0 and C2: x ^ 2 + y ^ 2 + d2x + e2y + F2 = 0
x^2+y^2+D1x+B1Y+F1+λ(x^2+y^2+D2X+E2Y+F2)=0 (λ≠-1)
❶ circle C2 is not included in this circle system equation. If the circle system equation is directly applied, it is necessary to check whether circle C2 meets the meaning of the problem and avoid missing solutions
❷ when λ = - 1, the linear equation of the common chord of two circles is obtained: (d1-d2) x + (B1-B2) y + (F1-F2) = 0
When reviewing the equation of the circle system above the circle system, the following three questions arise
1. For "&#; this circle system equation does not contain circle C2, if we apply this circle system equation directly, we must check whether circle C2 satisfies the meaning of the problem and guard against missing solutions. I mean, under what circumstances does the circle system equation not contain C2? Is the equation of C2 itself not a circle? Or something else?
2. In the characterization of "&#; when λ = - 1, we get the linear equation where the common chord of two circles lies: (d1-d2) x + (B1-B2) y + (F1-F2) = 0", if λ = - 1, then it means C1 = C2? In this way, there is x ^ 2 + y ^ 2 + D1X + b1y + F1 = x ^ 2 + y ^ 2 + d2x + e2y + F2; that is, D1 = D2, E1 = E2, F1 = F2. Since this is the case, is the linear equation (d1-d2) x + (B1-B2) y + (F1-F2) = 0 meaningful?
3. Is it necessary to give at least one intersection point in all the equations of circle system, whether it is the equation of two circles or the equation of a circle and a straight line, so as to get the value of λ?
I'm stupid, but please explain to me~
If I can solve these three problems well, I will add scores~

1. When λ = 0, there is no C2, and the equation of circle system is: x ^ 2 + y ^ 2 + D1X + b1y + F1 = 0, that is, C1; 2. When λ = - 1, the equation of line is obtained, that is, the line at the intersection of two circles, such as C1: x ^ 2 + y ^ 2 + 3x + 5Y + 2 = 0 and C2: x ^ 2 + y ^ 2 + 5x + 7Y + 4 = 0. The equation of line (d1-d2) x + (B1-B2) y + (F1-F2) = 0 is

The two focal points of the ellipse are F1F2. If there is a point P on the ellipse, which satisfies ∠ f1pf2 = 90 °, try to find the value range of eccentricity of the ellipse

[√2/2,1）
When e = √ 2 / 2 is, P is at the upper or lower vertex, and it is 90 at this time, which is also the largest focus triangle, it can be proved by cosine theorem. The larger e is, the flatter the ellipse is

Find the parabolic equation of length 8 of the chord AB whose vertex is at the origin, with X-axis as the symmetry axis, and whose focal point is perpendicular to x-axis, and point out its focal point coordinate and quasilinear equation

2p=8
Therefore, the equation is as follows:
(1) Y & # 178; = 8x, focus f (2,0), quasilinear equation: x = - 2;
(2) Y & # 178; = - 8x, focus f (- 2,0), quasilinear equation: x = 2;