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As shown in the figure, the parabola y = - X & # 178; + 2 (k-1) x + K + 1 intersects the X axis at two points a and B, and intersects the Y axis at point C. the length ratio of line OA to ob is 1:3 (1) Finding the analytic formula of parabola and the coordinates of two points a and B (2) The circle d with diameter AB intersects with the positive half axis of Y axis at point e. the tangent line of circle D is made through e, and the X axis intersects with point F. the coordinates of point F are calculated AB is on the opposite side of Y axis
The root formula shows that the ratio of X1 to X2 is equal to plus or minus 3
RELATED INFORMATIONS
- 1. If the two strings of a circle are parallel to each other, are the arcs between the two strings equal?
- 2. How to prove that the arcs of two equal strings are equal
- 3. The two arcs of the same string must be equal As above
- 4. In the same circle or equal circle, the arcs and chords opposite by equal circle angles are not equal There is another question: why is the degree of the arc equal to that of the central angle? Is the degree of an arc equal to that of a circle?
- 5. It is proved that the arcs added by two parallel strings of a circle are equal
- 6. If the parabola y = 2x2-4x-5 is translated 3 units to the left and 2 units to the upper, the parabola C is obtained, then the analytical formula of parabola c about Y-axis symmetry is______ ．
- 7. Given the parabola y = 2 (K + 1) x2 + 4kx + 2k-3, when we find out the value of K, the two intersections of the parabola and X axis are located on both sides of the origin? Answer x1x2
- 8. It is known that the two different intersections of the parabola y = AX2 + 2x + C and X-axis are on the right side of the origin, then the point m (a, c) is on the second side___ &Quadrant
- 9. If the parabola y = - x ^ 2 + 2 (k-1) x + 2k-k ^ 2 passes through the origin and opens downward, find: 1 the analytic expression of quadratic function 2. The area of triangle formed by intersection A.B and vertex C of X axis
- 10. Find the solution of parabola y = 2x square - 4x + 5 about X axis, Y axis, origin, vertex symmetry
- 11. A straight line with a slope of 1 intersects with a parabola y2 = 2x at two different points a and B. find the trajectory equation of the midpoint m of the line ab
- 12. It is known that the square of a straight line passing through point P (2,0) with a slope of 4 / 3 and a parabola y = 2x intersect at two points a and B. let the midpoint of line AB be M. Find the coordinates of point M. how to teach the students this problem, The answer seems to be m (41 / 16,3 / 4). How can I tell the students?
- 13. If we know that the square + (m-1) x + (m-2) of the parabola y = x intersects with the x-axis and two points a and B, and ab = 2, then what is m?
- 14. If the parabola C1C2 is symmetric about the Y-axis and the parabola C1: y = x ^ 2-3x + 2, then the analytical expression of the parabola C2 is
- 15. It is known that two parabola C1: y = x squared-4 and C2: y = x squared-2ax + B {a, B are constants} and The x-axis intersects at A1, B1 and A2, B2. The vertices are Q1 and Q2 respectively. It is known that the point P (a, b) is on the parabola C1 Try to explain the position relationship between two parabolas Judging the shape of quadrilateral a1q1q2a2 I hope I can help you. I really don't have any points now. I'm sorry
- 16. The vertex of parabola y = x2 + 3x is in () A. First quadrant B. second quadrant C. third quadrant D. fourth quadrant
- 17. If the line y = 3x + m passes through the first, third and fourth quadrants, then the vertex of the parabola y = (x-m) 2 + 1 must be at () A. First quadrant B. second quadrant C. third quadrant D. fourth quadrant
- 18. Translate the parabola y = ax (a ≠ 0) upward by three units, so that the length of its segment on the x-axis is 4, and find the value of A
- 19. If the parabola y = x ^ + PX + Q is shifted to the right by 3 units, and then to the right by 2 units, the following formula is obtained: y = x ^ - 3x + 15, then p, Q, etc?
- 20. If there are two points a and B on the parabola y = x2 + 4x-2, and the origin is at the midpoint of line a and B, then the coordinates of these two points are?