Given that the distance between a point P on the ellipse 3x2 + 4y2 = 12 and the left focus is 52, then the distance between the point P and the right guide line is 52______ .

Given that the distance between a point P on the ellipse 3x2 + 4y2 = 12 and the left focus is 52, then the distance between the point P and the right guide line is 52______ .

According to the definition of ellipse, the distance between P and the right focus is 4-52 = 32. According to the second definition of ellipse, the distance between P and the right guide line is 32e = 3
It is known that the eccentricity of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is 1 / 2, the distance from right focus to line L1 is 3 / 5, and the equation of ellipse C is solved
The answer is C = 1, so a = 2 why
The answer is that C = 1, so a = 2, because the centrifugal rate is 1 / 2, then E = A / C = 1 / 2
Given that the distance between the point P on the ellipse 3x square + 4Y square = 12 and the left focus is 2.5, find the distance from the point P to the right guide line
First, we change the equation into standard form, knowing that the focus is on the x-axis, we get a = 2, C = 1, so the eccentricity is e = C / a = 1 / 2, the right guide line is x = 4, and the left guide line is x = - 4. According to the second definition of ellipse, the distance from P to the left focus is 5 / 2 / D = e = 1 / 2, so we can get the distance from P to the left guide line d = 5, the distance between two guide lines is 8, so the distance from P to the right guide line is equal to 3
The line L passing through the right focus of ellipse C: 3x ^ 2 + 4Y ^ 2 = 12 intersects the ellipse at two points a ` B. if the sum of the distances from two points a ` B to the right guide line is 7, find the equation of line L
Let the equation of line l be y = K (x-1)
Substitute 3x ^ 2 + 4Y ^ 2 = 12 to get
3x^2+4k^2x^2-8k^2x+4k^2-12=0
The distance from point a to the right guide line is | x1-4 | = 4-x1
The distance from point B to the right guide line is | x2-4 | = 4-x2
And ∵ 4-x1 + 4-x2 = 7
∴x1+x2=1
And ∵ X1 + x2 = - (- 8K ^ 2) / (3 + 4K ^ 2)
∴8k^2=3+4k^2
∴k=±√3/2
∴y=±√3/2(x-1)
Given that the distance between the point P on the ellipse 3x2 + 4y2 = 12 and the left focus is 52, the distance between the point P and the right guide line is calculated
According to the definition of ellipse, the distance between P and the right focus is 4-52 = 32. According to the second definition of ellipse, the distance between P and the right guide line is 32e = 3
Ellipse C: X & # 178; / 6 + Y & # 178; / 4 = 1, the linear equation of chord AB with m (2,1) as the midpoint is?
Let the coordinates of point a be (C, d), then the coordinates of point B be (4-C, 2-D);
A and B are on the ellipse,
∴2c^2+3d^2=12 ①
2（4-c)^2+3(2-d)^2=12 ②
Results: C = (11-3d) / 4
By substituting the above formula into (1), we get: 33d ^ 2-66d + 25 = 0
Solution: D = 1 ± (2 √ 66 / 33)
∴c=2-（±√66/22)
The coordinates of point a are (2 + √ 66 / 22,1 - (2 √ 66 / 33) or (2 - √ 66 / 22,1 + 2 √ 66 / 33)
According to the analytic formula of line between two points, the analytic formula of line AB is obtained by substituting a and m
Given that the coordinates of the midpoint P of the chord ab of the ellipse x ^ 2 / 6 + y ^ 2 / 5 = 1 are (2, - 1), then the equation of the straight line AB is?
Let a (x1, Y1), B (X2, Y2), P (2, - 1), the slope of line AB be K,
If P is the midpoint of AB, X1 + x2 = 4, Y1 + y2 = - 2;
According to the elliptic equation, X1 & sup2 / 6 + Y1 & sup2 / 5 = 1, and X2 & sup2 / 6 + Y2 & sup2 / 5 = 1,
5 (x1 & sup2; - x2 & sup2;) + 6 (Y1 & sup2; - Y2 & sup2;) = 0
5(x1+x2)(x1-x2)+6(y1+y2)(y1-y2)=0
20-12k = 0, i.e. k = 5 / 3,
And the line AB passes through the point P (2, - 1),
It can be seen from the point oblique formula of the linear equation that y + 1 = (5 / 3) (X-2),
The equation of line AB is 5x-3y-13 = 0
5x-3y=13.
Find the elliptic standard equation with the same focus as the ellipse X & # 178; / 9 + Y & # 178; / 4 = 1 through point (3, - 2)
Let the equation be X & # 178; / (9 + k) + Y & # 178; / (4 + k) = 1
Dai Ren (3, - 2) de
9/(9+k)+4/(4+k)=1
The solution is: k = 6, k = - 6
The equation is: X & # 178 / 15 + Y & # 178 / 10 = 1
What is the elliptic standard equation with the same focal point as the ellipse X & # 178; / 9 + Y & # 178; / 4 = 1 and passing through point (3, - 2)
Let the equation be: X & # 178; / (9 + k) + Y & # 178; / (4 + k) = 1
Dai Ren (3, - 2) de
9/(9+k)+4/(4+k)=1
The solution is k = 6
∴x²/15+y²/10=1
Given that the distance from a point P on the ellipse X & # 178; / 25 + Y & # 178; / 9 = 1 to the left focus F1 is 2, q is the midpoint of Pf1, O is the origin of the coordinate, find the length of OQ
Let the right focus of the ellipse be F2 and connect PF2
P is the point on the ellipse
∴|PF1|+|PF2|=2a=10
The distance between point P and left focus F1 is 2
∴|PF1|=2
∴|PF2|=8
∵ o is the midpoint of | F1F2 | and Q is the midpoint of | Pf1 |
The OQ is the median of △ f1pf2
∴|OQ|=(1/2)|PF2|=4.