7. Ellipse () represented by equation (a > b > 0, k > 0 and k≠ 1) and equation (a > b > 0).
A. have the same quirks; B. Have the same focus; C. there is a short axis and a long axis of equal length; Have the same vertex.
8 (12) It is known that the eccentricity of an ellipse is that a straight line passing through the right focus and having a slope intersects at two points. If so, then ().
(A) 1 (B) (C) (D)2
9 If the major axis length, minor axis length and focal length of an ellipse are arithmetic progression, then the eccentricity of the ellipse is ().
A.B. C. D。
10 If point O and point F are the center and left focus of the ellipse respectively, and point P is any point on the ellipse, the maximum value of is ().
A.2 B.3 C.6 D.8
1 1 The right focus of the ellipse is f, and the intersection of its right directrix and the axis is. If a point p on the ellipse intersects with the intersection point f of the middle vertical line of the line segment AP, the range of eccentricity of the ellipse is ().
(A)(0，)
(B)(0，)
(3)
C.
Fill in the blanks: (This big question is ***4 small questions, *** 16 points. )
13 If the length of the major axis and the length and focal length of the minor axis of an ellipse are arithmetic progression, then the eccentricity of the ellipse is
The angle formed by a point p on the ellipse 14 and a straight line connecting the two focal points F 1 and F2 of the ellipse is a right angle, so the area of Rt△PF 1F2 is.
15 is known as the focus of the ellipse, the endpoint of the short axis, and the extension line of the line segment intersect with a point, and the eccentricity of the line segment is.
16 It is known that the two focuses of an ellipse are 0, and the points satisfy, then the value range of ||+| is _ _ _ _ _.
Third, the solution: (This big topic is ***6 small questions, and the score is ***74. The solution should be written in proof process or calculus steps. )
17.( 12 point) It is known that the point m is on the ellipse, m is perpendicular to the line where the ellipse focuses, and m is the midpoint of the line segment. Find the trajectory equation of this point.
18.( 12 point) The focus of the ellipse is and respectively. It is known that the eccentricity of an ellipse passes through the center of the circle as a straight line, and the intersection with the ellipse at two points A and B is the origin. If the area is 20, find the value of (1). (2) Equation of straight line AB.
19( 12 point), which are the left and right focal points of the ellipse respectively. The straight line intersects the ellipse at two points, with an inclination of, and a distance of.
(i) Find the focal length of the ellipse;
(2) If, find the equation of ellipse.
20( 12 point) Let the left focus of ellipse C be f, the straight line passing through point F intersects ellipse C at points A and B, and the inclination of straight line L is 60o.
Find the eccentricity of ellipse c;
If |AB|=, find the equation of ellipse C.
2 1( 12 minutes) in the plane rectangular coordinate system xOy, point b and point a (-1, 1) are symmetrical about the origin o, p is the moving point, and the slope product of the straight line AP and BP is equal to.
(i) Find the trajectory equation of the moving point p;
(ii) Let the straight lines AP and BP intersect with the straight line x=3 at points M and N respectively. Q: Is there a point P that makes the areas of △PAB and △PMN equal? If it exists, find the coordinates of point P; If it does not exist, explain why.
22 (14 point) known ellipse (A >；; B>0), the area of the diamond obtained by connecting the four vertices of the ellipse is 4.
(i) Find the equation of ellipse;
(2) Let the straight line L intersect the ellipse at two different points A and B, and the coordinates of point A are known as (-a, 0).
(i) If yes, find the inclination angle of the straight line L;
(ii) If the point q is located on the perpendicular bisector of the line segment AB, and.
Ellipse (2) Reference Answer
1. Multiple choice question:
The title is123455678911112.
The answers are BBB, BCB, BCB, BCD, BCD.
Propositional intention This topic mainly examines the nature and second definition of ellipse.
Analytically, let the straight line L be an elliptic directrix, e be eccentricity, let A and B be AA 1, BB 1 be perpendicular to L, A 1, and B be perpendicular to AA 1 and E, which is defined by the second definition.
That is k=, so choose B.
nine
10 analysis from the meaning of the question, f (- 1 0), set point p, then there is, solution,
Because,, so
= =, the parabola symmetry axis corresponding to this quadratic function is because, at that time, take the maximum value and choose C.
Proposition intention This topic examines the equation, geometric properties, coordinate operation of the product of plane vectors, monotonicity and maximum value of quadratic functions, etc. To examine students' proficiency in the basic knowledge of the program and their comprehensive application ability and operation ability.
1 1 analysis: according to the meaning of the question, there is a point p on the ellipse, so that the midline of the line segment AP passes through this point.
That is, the distance from point f to point p is equal to point a.
And | fa | =
|PF|∈
C.
Fill in the blanks: (This big question is ***4 small questions, *** 16 points. )
13 If the length of the major axis and the length and focal length of the minor axis of an ellipse are arithmetic progression, then the eccentricity of the ellipse is
The angle formed by a point p on the ellipse 14 and a straight line connecting the two focal points F 1 and F2 of the ellipse is a right angle, so the area of Rt△PF 1F2 is.
15 (20 10 National Volume 1) (16) It is known that the focus of the ellipse, the endpoint of the short axis, the extension of the line segment intersect with a point, and the eccentricity of the line segment is.