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The parabola y = - 3 / 4x ^ 2 + 3 intersects the x-axis at points a and B, the straight line y = - 3 / 4x + B intersects at points B and C, and the straight line y = - 3 / 4x + B intersects the y-axis at points E (1) Write the analytical expression of the straight line BC (2) Finding the area of △ ABC (3) If point m moves from a to B at the speed of one unit length per second on line AB (not coincident with a and b), and point n moves from B to C at the speed of two units length per second on ray BC. Let the motion time be T seconds, write out the functional relationship between the area s of △ MNB and T, and find out the maximum area of △ MNB when point m moves for how long?
As shown in the picture
Given that the parabola y ^ 2 = 4x, the line L passing through the point m (0,2) intersects the parabola at two points a and B, and the line L intersects the X axis at point C
1) You first use the similar shape to describe the following: XC / XB = XC / XB = XA / XC a (XA, ya) B (XB, Yb) B (XB, Yb) and then set the linear equation y = K (x-xc) this way, you have to explain that the slope does not exist, the situation can't intersect with AB, and then you can use the similar shape to describe the following: first, you use the similar shape to describe the following: XC / XB = XC / XB = XC / XB = XC / XB = XA / XB = XA / XB = XA / XB = XA / XB = XA = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = 4x = K / 4Y ^ 2 / 4Y ^ 2 / 4Y ^ 2 / 4Y ^ 2-y ^ 2-y ^ 2-y ^ 2-y ^ 2-y ^ 2-y it is proved that the vector Ma = α vector AC, Vector MB = β vector BC MB vector = MC vector + CB vector note that the vector is a vector, and the vector is a vector
RELATED INFORMATIONS
- 1. If the line passing through the focus F of the parabola y2 = 4x intersects with the parabola at two points a and B, then OA · ob=______ ．
- 2. The distance from the focus of the parabola y = 4x2 to the collimator is______ ．
- 3. It is known that the equation of the line where the edge CD of square ABCD is located is x-3y-4 = 0, the intersection point of diagonal AC and BD is p (5.2) It is known that the equation of the line where the edge CD of square ABCD is located is x-3y-4 = 0, the intersection point of diagonal AC and BD is p (5.2) Solving the equation of the line where AB edge is located The equation for finding the circumcircle of square ABCD
- 4. Two diagonals of rectangle ABCD intersect at M (2,0) AB side, the linear equation is x-3y-6 = 0 point t (- 1,1) on the straight line of AD, the moving circle P passes through n Two diagonals of rectangle ABCD intersect at the edge of M (2,0) AB, and the linear equation is x-3y-6 = 0 point t (- 1,1). On the straight line where ad is located, the moving circle P passes through n (- 2,0) and is circumscribed with the circumscribed circle of ABCD, and the trajectory equation of the center of the moving circle is obtained
- 5. Make a straight line through the point m (0,1) so that the line segment cut by two straight lines L1: x-3y + 10 = 0, L2: 2x + Y-8 = 0 is exactly bisected by m, and solve the linear equation
- 6. Given that two points a and B are on the line 2x-y = 0 and X + 2Y = 0 respectively, and the midpoint of AB segment is p (0,5), then the length of AB segment is______ ．
- 7. Make a straight line L through point a (- 1,1) so that the midpoint of the line segment cut by two parallel lines L1: x + 2y-1 = 0 and: x + 2y-3 = 3 is exactly on the straight line L3: x-y-1 = 0, The equation for finding the line L
- 8. The center is the origin, and the two focal points have a point P (3, t) on the ellipse on the x-axis. If the distance between the point P and the two focal points is 6.5 and 3.5 respectively, the elliptic equation is solved
- 9. If the center of the moving circle is on the parabola y2 = 8x and the moving circle is always tangent to the straight line x + 2 = 0, then the moving circle must pass the fixed point------ Another problem: in the plane rectangular coordinate system xoy, two fixed points a and B on the parabola y2 = 4x which are different from the coordinate origin o are satisfied with AO vertical Bo, and the trajectory equation of the center of gravity g of the triangle AOB is obtained How to answer these two questions? How to find out?
- 10. The center F of the circle M: x = 1 + cos θ is a parabola e: x = 2pt & sup2; the focal point of the circle M: x = 1 + cos θ is a straight line intersection parabola e passing through the focal point F at two points y = sin θ y = 2pt Find the value range of afbf The center F of the circle M: x = 1 + cos θ y = sin θ is a parabola e: x = 2pt & sup2; the focal point of y = 2pt passes through the straight line intersection parabola e of the focal point F, and the value range of AF · BF is calculated at two points ab
- 11. The image of quadratic function y = x ^ 2-2x 5 is folded along the y-axis to obtain the analytical expression of the parabola
- 12. The parabola y = ax square + BX + C, when x = 2, x = 0, the value of Y is equal The parabola y = ax square + BX + C, when x = 2, x = 0, the value of Y is equal, the vertex m of the parabola is on the straight line y = 3x-7, and the abscissa of the intersection point with the straight line is 4 Find the analytic formula of this parabola
- 13. Given the parabola y = ax square + BX + C, | a | = 1 / 2, the coordinates of the highest point are (* 1,5 / 2), find the value of a.b.c
- 14. If the parabola y = ax square + BX + C passes through (2,0) (0,2) (- 1,0) 3 points, its analytical formula is
- 15. It is known that the square of parabola y = ax + BX + C (a is less than 0) passes through point a (- 2,0), O (0,0) We know the square of parabola y = ax + BX + C (a)
- 16. If the distance between a point m on the parabola y ^ 2 = 3x and the coordinate origin o is 2, then the distance between the point m and the focus of the parabola is 2_____ .
- 17. Parabola y = 4x, straight line y = X-1 and parabola intersect at two points a and B, calculate triangle OAB area, O is the origin
- 18. As shown in the figure, in the plane rectangular coordinate system, a (- 3,0), point C is on the positive half axis of Y axis, BC ‖ X axis, and BC = 5, AB intersects Y axis at point D, OD = 32 (1) (2) the parabola passing through three points a, C and B intersects with the x-axis at point E and connects with be. If the moving point m starts from point a and moves in the positive direction of x-axis, and the moving point n starts from point E and moves at a constant speed on the straight line EB, the moving speed is one unit length per second. When the moving time t is, the △ mon is a right triangle
- 19. It is known that the image with inverse scale function y = 1 / X and primary function y = 2x-1 has an intersection point a (1, a). Whether there is a point P on the x-axis makes the triangle POA isosceles Triangle? If it exists, find out the coordinates of point P. if not, explain the reason
- 20. It's very urgent. The parabola y = ax-3ax + 3 intersects the x-axis at a (- 1,0) B (4,0) intersects the y-axis at C The square of parabola y = ax - 3ax + 3 intersects X axis at a (- 1,0) B (4,0) intersects Y axis at C. 1. Find the analytical formula of parabola 2. Translate the parabola along the Y-axis and intersect the y-axis at point D. when BD = 2CD, find the coordinates of point D 3. If the parabola is folded along the straight line x = m, make the folded parabola intersecting straight line BC at two points P and Q, and P and Q are symmetrical about point C, draw the value graph of m by yourself. Because I don't have a picture