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It is known that the eccentricity e of ellipse C: x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is 1 / 2, and the distance from origin o to straight line X / A + Y / b = 1 is d = (2 √ 21) / 7 The equation of ellipse is x ^ 2 / 4 + y ^ 2 / 3 = 1 Solution: make a straight line through point m (√ 3,0) and intersect ellipse C at two points P and Q, and find the maximum area of △ OPQ
The area of △ OPQ can be divided into △ mop and △ MOQ. With OM as the bottom and the absolute value of the ordinate of P and the absolute value of the ordinate of Q as the high, then s △ OPQ = | om |||||| yp-yq | / 2 is set as a straight line analytical expression, which is connected with the elliptic equation
RELATED INFORMATIONS
- 1. On the number axis, which side of the origin is the point representing the number 6, and the distance to the origin is several unit lengths; the distance from the point representing the number 6 to the point representing the number-8 is Several units of length
- 2. On the number axis, the distance to the origin is the root sign, and the number of 6 is
- 3. On the number axis, the point of - 5 is at the beginning of the origin___ Side, the distance from the origin is___ . the distance from the origin is 4 units of length__ Yes, they are___ On the number axis, a point five units in length away from the point representing - 2 is the same as the number represented____ ? Simplification: 1 - 2=____ ? -The absolute value of 4.7 is____ The number whose absolute value is 3 and 1 / 5 is___ ? The number with the smallest absolute value is__ The number whose absolute value equals itself is____ ? Given x = 8, y = - 2, find the value of x-4, y Comparison size: 1 + 5___ - 6; 1 - 100___ -（-101）. All integers greater than - 3 and less than 2 are___ ? Fill in the appropriate integer in the following box to make the formula true: - 3 ＜ mouth ＜ - 1.5 ＜ mouth ＜ 0 ＜ mouth ＜ 2 Given a = 4, B = 3 and a < B, try to find the value of a and B
- 4. Given point P (2, - 1), what is the maximum distance between point P and the origin Why is the maximum distance OP?
- 5. If the point P (2, - 1) is known, the equation of the line L which passes through the point P and has the largest distance from the origin is obtained, and the maximum distance is obtained;
- 6. Find the trajectory equation of the point with the same distance between two lines 2x-y-1 = 0 and 4x-2y + 9 = 0
- 7. The trajectory equation of the point with equal distance to the line y = 0 and the line y = √ 3 (x + 1), The answer is (√ 3x-3y + √ 3) (√ 3x + y + √ 3) = 0 I'm dull and love to get to the top of things, so the more detailed the better,
- 8. Make two mutually perpendicular straight lines L1 and L2 through point P (2,4). If L1 intersects X-axis at point a and L2 intersects Y-axis at point B, find the trajectory equation of the midpoint m of line ab
- 9. It is known that the line l1:4x-3y + 6 equals zero, the line L2: x equals minus 1, and the square of the parabola y equals the moving point P on 4x to the straight line It is known that the line L1: 4x minus 3Y plus 6 equals zero, the line L2: x equals minus 1, and the square of the parabola y equals the sum of the distances from the moving point P on 4x to the line L1 and the line L2? A. 1 B.3 c.d.16 molecule 37
- 10. It is known that the minimum value of the sum of the distances from the moving point P on the parabola y2 = 4x to the lines L1 and L2 is () A. 2B. 3C. 115D. 3716
- 11. It is known that the eccentricity of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) e = √ 6 / 3, and the distance between the line passing through points a (0, b) and B (a, 0) and the origin is √ 3 / 2 Given the fixed point E (- 1,0), if the line y = KX + 2 (K ≠ 0) intersects the ellipse at two points c and D, ask: is there a value of K to make the circle with diameter CD pass through point e? Please explain the reason
- 12. It is known that the eccentricity e of ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 (a > b > 0) is √ 6 / 3, and the distance between the straight line passing through points a (0, - b) and B (a, 0) and the origin is √ 3 / 2 (1) The equation of finding ellipse (2) Given the fixed point E (- 1), if the line y = KX + 2 (K ≠ 0) intersects the ellipse at two points c and D, ask: is there a value of K to make the circle with diameter CD pass through point e? Please explain the reason If it's right, answer the second question. If it's not right, write it all, E (- 1,0), sorry, I haven't finished
- 13. It is known that the eccentricity of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is √ 3 / 2, and the distance from the straight line passing through two points a (a, 0) B (0, - b) to the origin is four fifths of the root sign 5. The standard equation of the ellipse is solved
- 14. There is a point P on the number axis and its coordinate is X. if the distance between the known point P and the origin is less than 8, then x is X
- 15. What is the distance from the point P (- 3, - 4) to the X axis, to the Y axis, and to the origin
- 16. Given 2x + 3y-4z = 0, 3x + 3Y + 5Z = 0, find the value of X + y + X / X-Y + Z
- 17. The distance from the origin to the line x + 2y-5 = 0 is___ ．
- 18. Find a point P on the line x + 2Y = 0 so that its distance to the origin is equal to the distance of the line x + 2y-3 = 0
- 19. Coordinate origin to line 3x-2y + 1 = 0 to distance
- 20. Point a (- 1, - 2), B (3,6), find point P (x, y) on the straight line L: 3x + 3y-10 = 0, so that the distance difference between point 1 P and point a, B is the largest Answer (- 101 / 6121 / 6) detailed process