The focus of ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1 is f1.f2, and the point P is the moving point. When the angle f1pf2 is an obtuse angle, the abscissa of point P is________ ?

The focus of ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1 is f1.f2, and the point P is the moving point. When the angle f1pf2 is an obtuse angle, the abscissa of point P is________ ?

Then the range of ∠ f1pf2 is (90180)
: when ∠ = 90
Let P (3sin θ, 2cos θ)
From Pf1 ⊥ PF2
→2cos²θ/(9sinθ²-5)=-1
→sinθ=√5/5
→P(√5/5,cosθ)
When ∠ f1pf2 = 180, P (3,0)
→ target ε (√ 5 / 5,3)

If the line ax-y + 1 = 0 passes through the focus of the parabola x = 1 / 4Y ^ 2, then the real number a =?

Parabola x = 1 / 4Y ^ 2
The standard equation is: Y & # 178; = 4x
The focus is (1,0)
Substituting into the straight line: a + 1 = 0
So, a = - 1

If M is known to be a real number and a focus of ellipse x ^ 2 / 3 + y ^ 2 / M = 1 is the focus of parabola y ^ 2 = 4x, then M =?

The focus of the parabola y ^ 2 = 4x is (1,0)
A focus of ellipse x ^ 2 / 3 + y ^ 2 / M = 1 is (1,0)
c=1,a^2=3,b^2=m
m=a^2-c^2=2

It is known that the square of the parabola y = ax - 4x + C passes through the point a (0. - 6) B (3. - 9)
1. Find the analytical formula of parabola
2. Write the equation of symmetry axis and vertex coordinates of parabola
3. Point P (m, m) and point q are both on the function image (where m > 0), and these two points are symmetric about the parabola's symmetry axis. Find the value of M and the distance from point Q to X axis

It is known that the square of the parabola y = ax - 4x + C passes through the point a (0. - 6) B (3. - 9)
c=-6
-9=9a-12-6 a=1
(1) The square of parabolic analytic formula y = x-4x-6
2. Write the equation of symmetry axis and vertex coordinates of parabola
The square of y = x-4x-6
=(x-2)^2-10
Axis of symmetry equation x = 2
Vertex coordinates (2, - 10)
3. Point P (m, m) and point q are both on the function image (where m > 0), and these two points are symmetric about the parabola's symmetry axis. Find the value of M and the distance from point Q to X axis
p（m,m）
m=m^2-4m-6
m^2-5m-6=0
(m-6)(m+1)=0
M = 6 or M = - 1
(1) M = 6 p (6,6) axis of symmetry x = 2 Q (- 2,6) distance from point Q to X axis = 6
(2) M = - 1 p (- 1, - 1) axis of symmetry x = 2 Q (3, - 1) distance from point Q to X axis = 1