The focus coordinates of the ellipse X25 + y24 = 1 are______ ．

The focus coordinates of the ellipse X25 + y24 = 1 are______ ．

∵ ellipse X25 + y24 = 1, ∵ A2 = 5, B2 = 4, ∵ C = 5 − 4 = 1, ∵ the focus of ellipse is (1,0) and (- 1,0). So the answers are: (1,0) and (- 1,0)

Let the focus of the ellipse X & # 178; / A & # 178; + Y & # 178; / (1-A & # 178;) = 1 be on the x-axis
Let F 1 and F 2 be the left and right focal points on the x-axis, p be the point in the first quadrant of the ellipse, and f 2p intersect Y-axis on Q and f 1p ⊥ f 1q

Let the ellipse C: X & # 178 / / A & # 178; + Y & # 178 / / B & # 178; = 1 (a > b > 0) pass through the point m (√ 2,1), and the left focus is F1 (- √ 2,0)
(1) Find the equation of elliptic square C;
(2) When the moving line L passing through the point P (4,1) intersects with the ellipse C at two different points a and B, take Q on the line AB to satisfy ab ·qb = AQ ·pb (the module of AB vector multiplied by the module of QB vector = the module of AQ vector multiplied by the module of Pb vector). It is proved that the point q is always on a certain line

(1) As the left focus is F1 (- {2,2,0 -- \\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\\

If the line passing through a focus F1 of 4x + 2Y = 1 and the ellipse are compared with two points a and B, then a and B form a triangle with another focus F2 of the ellipse
What is the circumference of abf2

y²/(√2/2)² + x²/(1/2)² = 1
According to the definition of ellipse, the sum of the distances from the plane to two fixed points (focus) is the locus of the fixed point (2a)
∴|AF1|+|AF2|=|BF1|+|BF2|=2a=√2
∴|AF1|+|BF1|+|AF2|+|BF2|=2√2
That is, C = | ab | + | af2 | + | BF2 | = 2 √ 2