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If the distance between a point P and its focus on the parabola x ^ 2 = 4Y is 2, then the distance between point P and its directrix is 2
The distance from the point on the parabola to the focus is equal to the distance from the point to the directrix. In this problem, the distance from point P to the directrix is also 2
If the distance from a point (m, - 3) on the parabola x2 = - 2PY (P > 0) to its focus is equal to 5, then the value of M is?
The distance from a point (m, - 3) on the parabola X & # 178; = - 2PY (P > 0) to its focus is equal to 5,
Then the distance from it to the directrix y = P / 2 is also equal to 5,
That is, P / 2 - (- 3) = 5, P = 4
Thus (m, - 3) is substituted into the equation x & # - 178; = - 8y to obtain M = ± 2 √ 6
The distance from the focus of the parabola X & # 178; = - 4Y to its directrix is equal to ()
Focus coordinates (0, - P / 2)
Quasilinear equation y = P / 2
The distance between the focus and its guide line is p
Parabola X & # 178; = - 4Y P = 2
The distance between the focus of the parabola X & # 178; = - 4Y and its directrix is equal to (2)
RELATED INFORMATIONS
- 1. Let a (x1, Y1), B (X2, Y2), then x1x2 =? Let a (x1, Y1) and B (X2, Y2) pass through the focus of the parabola (x ^ 2) = 4Y to make the chord AB, then what is X1 times x2? There is a process or a graph.
- 2. How to find the directrix and focus of parabola? How to find the known parabola, collimator and focus? It is how to deduce the focal point and collimator of a parabola, or how to deduce a parabola from the focal point and collimator, just as the elliptic standard equation is derived by arithmetic and algebra.
- 3. Let a straight line passing through the focus of the parabola y2 = 2px (P > 0) intersect with the parabola. Let the coordinates of the two intersections be a (x1, Y1) and B (X2, Y2) respectively. Prove: (1) y1y2 = - P2 (2) x1x2 = p24
- 4. It is known that the center of ellipse C is at the origin and the focus is on the x-axis. The coordinates of a vertex B of ellipse C are (0,1) and the eccentricity is equal to 22. The line L with slope 1 intersects ellipse C at two points m and n. (1) find the equation of ellipse C; (2) ask whether the right focus F of ellipse C can be the center of gravity of △ BMN? If possible, find out the equation of line L; if not, explain the reason
- 5. If P (2,2) is the midpoint of AB, then the equation of parabola C is______ ．
- 6. The left focus of the ellipse is (√ 3,0), and the right vertex is d (2,0). Let a (1,1 / 2) be a moving point on the ellipse. If P is a moving point on the ellipse, find the trajectory equation of the midpoint m of the line PA
- 7. Given that the distance from a point P on the parabola y2 = 16x to the x-axis is 12, then the distance from P to the focus f is equal to 12______ ．
- 8. As shown in the figure, the straight line AB; CD intersects at the point O, OE, bisecting the angle AOC, and the angle BOC - ∠ BOD = 18 ° to find the degree of ∠ BOE
- 9. As shown in the figure, points a, O and B are on the same straight line, ∠ AOC = 1 / 2 ∠ BOC + 30 °, OE bisects ∠ BOC, and calculates the degree of BOE I don't know how to draw or dictate a straight line. The right side is B and the left side is a. there is o point in the middle, with o as the point, extending from the upper right corner to e and from the upper left corner to C~
- 10. As shown in the figure, it is known that OE is the bisector of ∠ AOB, and C is a point in ∠ AOE. If ∠ BOC = 2 ∠ AOC, ∠ AOB = 114 °, calculate the degree of ∠ BOC. ∠ EOC
- 11. If the distance from a point m on the parabola x ^ 2 = - 16y to the focus is 6, then the coordinate of M is
- 12. Given that the distance from the point P on the parabola x2 = 4Y to the focus is 10, then the coordinate of point P is 0______ ．
- 13. If a ＜ 0, the vertex of the parabola y = x * + 2aX + 1 + 2A * is in the? Th quadrant
- 14. When a
- 15. It is known that the vertex m of the parabola y = AX2 + BX + C with downward opening is in the second quadrant And through the points a (1,0), B (0,1) (1) Please judge the value range of real number a and explain the reason (2) Let the other intersection of the parabola and the x-axis be c. when the area of △ AMC is 25 / 16 times of the area of △ ABC, a is obtained
- 16. Generally, we can use formula to find the vertex and symmetry axis of parabola y = ax ^ 2 + BX + C (a ≠ 0). Y = ax ^ 2 + BX + C = a [x + (B / 2a)] ^ 2+ Generally, we can find the vertex and symmetry axis of parabola y = ax ^ 2 + BX + C (a ≠ 0) y=ax^2 + bx + c =a[x+(b/2a)]^2 + (4ac-b^2)/4a, y=ax^2 + bx + c It should not be converted to (x + B / 2a) ^ 2 = B ^ 2-4ac / 4A ^ 2. How can it be converted to the above form?
- 17. The vertex of the parabola y = AX2 + BX + C is on the Y-axis and passes through two points - (- 1,3), (- 2,6)
- 18. Parabola y = - 4 (x + 3) square, when x_____ The value of function y increases with the increase of X_____ The value of function y decreases with the increase of X, and the square of parabola y = - 4 (x + 3) can be changed from the plane direction of parabola y = - 4x_____ Translation_____ Units get it!
- 19. The distance from the image vertex of quadratic function y = ax ^ 2 + K to the X axis is 3, and the shape is the same as that of parabola y = x ^ 2
- 20. 6. If the parabola y = ax & # 178; + BX + C (a is not equal to 0) passes through the points a (- 1,0), B (3,0), then the symmetric axis of the parabola is a straight line, and the analytic function is?