In a parabola, the distance from the focus to the collimator is 4, and the focus is on the y-axis. Write out the standard equation of the parabola and find the solution

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• 1. Write the standard equation of parabola according to the following conditions: (1) the focal point is f (0,3), (2) the distance from the focal point to the collimator is 2
• 2. Given that the vertex is at the origin and the focus is on the Y-axis of the parabola C section line y = 2x-1, the chord length is 2 root sign 10, and the equation of parabola C is obtained
• 3. Through the focus F of parabola y2 = 4ax (a > 0), make two mutually perpendicular focus chords AB and CD, and find the minimum value of | ab | + | CD |
• 4. Make a straight line with a slope of 45 degrees through the focus f with the square of parabola y = 4x, intersect the parabola at two points a and B, and find the distance from the midpoint C of AB to the parabola collimator
• 5. Given the parabola y & sup2; = 4x, make a straight line with an inclination angle of π / 4 through its focus F, intersect the parabola at two points a and B, let the vertex of the parabola be o, and find △ a Given the parabola y & # 178; = 4x, make a straight line through its focus f with an inclination angle of π / 4, intersect the parabola at two points a and B, let the vertex of the parabola be o, and calculate the area of △ ABC
• 6. Given that the inclination angle of the line passing through the focus of the parabola y ^ 2 = 4x is 60 degrees, then the distance from the vertex to the line is?
• 7. Through the focus F of the parabola y ^ 2 = 4x, make a straight line intersection parabola with an inclination angle of θ, and use θ to represent the length of AB at two points ab
• 8. The parabolic standard equation with chord length of 16, which is perpendicular to the x-axis and has the focal point, is solved
• 9. (y ^ 3-4x ^ 2) / (x ^ 3 + 2Y) = 44 / 31 given DX / dt = 5 x = - 3 y = - 2 find dy / DT
• 10. Solve DX / (x + T) = dy / (- y + T) = DT
• 11. Find the standard equation of a parabola satisfying the following conditions. On the parabola y ^ 2 = 24ax (a > 0), there is a point m whose abscissa is 3 and its distance from the focus is 5
• 12. Translate the square of the parabola y = 2x left and right so that it intersects the X axis at point a and the Y axis at point B. if the area of △ AOB is 8, find the analytical formula of the parabola after translation
• 13. Parabola y = 2x ^ 2 + 1 and parabola y = - 2x ^ 2 + k are at most the same_____ Intersection points
• 14. It is known that the parabola y = (k-1) x2 + 2kx + K-2 has two different intersections with the X axis (1) (2) when k is an integer and the solution of the equation 3x = kx-1 about X is negative, find the analytical formula of the parabola; (3) under the condition of (2), if you draw the largest square in the closed graph surrounded by the parabola and X axis, so that one side of the square is on the X axis and the two ends of the opposite side are on the parabola, try to find the largest square What's your side length?
• 15. It is known that the parabola y = 2x2 + 4x + k-1 has two intersections with the x-axis
• 16. If the parabola y = (1-k) x ^ 2-2x-1 has two intersections with the X axis, then the value range of K is the same RT
• 17. It is known that the parabola y = x2 square-2x-8. The two intersections of the parabola and the X axis are a and B respectively (a is on the left side of B), and its vertex is p. find the surface of the triangle ABP
• 18. The coordinates of the intersection of the parabola 2x ^ 2-3x-5 and the X axis are
• 19. Using image to find the coordinates of the intersection of the square + 3x + 5 of parabola y = - 2x and X axis
• 20. Is there an intersection between the parabola y = x2-2x-3 and y = x + 1? If so, find the coordinates of the intersection