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The coordinates of the center P of a circle (- 2,5), and its radius is 6, then the origin of the coordinates is at point P
The distance from the center of the circle to the origin of the coordinates is root 29, which is less than 6
In the plane rectangular coordinate system, 0 is the coordinate origin, and the circle with 0 as its center is tangent to the straight line x-radical 3y-4 = 0 1. Find the circle 0 equation 2. The straight line L: y = KX + 3 and circle 0 intersect at two points A. B. whether there is a point m on circle 0, so that the quadrilateral oamb is diamond. If there is, calculate the slope of the straight line L; if not, please explain the reason
1. If the radius of the circle is r, then the tangent result is: the distance from o point to the straight line X - √ 3y-4 = 0 = R; | 0 - √ 3 × 0-4 / √ (1 + 3) = R; r = 2, so the equation of the circle is: x ﹣ y ﹤ 4; 2
O is the coordinate origin, and the coordinate of a is (1, root 3) 1: A reward of 100 seconds is offered: O is the origin of coordinates, the coordinate of a is (1, the root 3), M is the point on the coordinate axis, and the triangle MOA is an isosceles triangle. How many points meet the conditions? A4 B5 C6 D8
Six were (- 2,0) (2,0) (0,2) (0, - 2) (0,2 √ 3 / 3) (0,2 √ 3)
OA = OM, OA = am, OM = am, three cases are OK
It is known that an ellipse in a plane rectangular coordinate system has its center at the origin and its left focus is f (- Set point a (1, 1) through D (2, 0) 2）． (1) Find the standard equation of the ellipse; (2) If P is a moving point on an ellipse, the trajectory equation of point m in line PA is obtained
(1) ∵ for an ellipse in a plane rectangular coordinate system, its center is at the origin, the left focus is f (- 3, 0), and through D (2,0), ᙽ the semimajor axis of the ellipse a = 2, the half focal length C = 3, then the semi minor axis B = 1.
In the plane rectangular coordinate system, if the focal length of the ellipse x ^ 2 / A ^ 2 + y ^ 2 / b ^ 2 = 1 (a > b > 0) is 2, the circle with o as the center and a as the radius, and the two tangent lines of the circle passing through the point (a ^ 2 / C, 0) are perpendicular to each other, then the eccentricity e = It's better to have a detailed solution. It's not possible to get a number of answers The title was given to me. I don't know right or wrong, but thank you
The problem is right. It's easy to draw a picture
∵a√2=a^2/c
∴c/a=1/√2=√2/2=e
In the plane rectangular coordinate system, the relationship between the position of point B (1,4) and the circle with (2,3) as its center and 2 as its radius
See the center distance and radius
(2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (2) = (
In the plane rectangular coordinate system, Xiao Fang draws a circle with point a (0, - 3) as its center and 3 as its radius
The equation of a circle
x²+(y+3)²=9
When x = 0
(y+3)²=9
Y + 3 = 3 or y + 3 = - 3
Y = 0 or y = - 6
So the intersection with the Y axis is (0,0) and (0, - 6)
In fact, it's OK to do it directly,
Let the intersection point (0, m)
Then | m + 3 | = 3
M = 0 or M = - 6
So the intersection with the Y axis is (0,0) and (0, - 6)
In a rectangular coordinate system, a circle is drawn with (0,4) as its center and 3 as its radius As above
(0,7) (0,1) kindergarten questions
Draw ⊙ B with B (0,3) as the center and 6 as the radius to find the intersection coordinates of the circle and the coordinate axis
Because B (0,3) is the center of the circle and the radius is 6
So the equation of circle B is: x ^ 2 + (Y-3) ^ 2 = 36
When x = 0, (Y-3) ^ 2 = 36, y = 9 or y = - 3
When y = 0, x ^ 2 = 36, x = 6 or x = - 6
So the coordinates of the intersection of the circle and the axis are
(0,9) (0,-3) (6,0) (-6,0)
I think the process is wordy enough
In the plane rectangular coordinate system xoy, it is noted that there are three intersections between the quadratic function f (x) = x2 + 2x + B (x ∈ R) and two coordinate axes. The circle passing through the three intersections is denoted as C (1) Find the value range of real number B; (2) Find the equation of circle C; (3) Does circle C pass through a fixed point (its coordinates are independent of B)? Please prove your conclusion
(1) let x = 0, the intersection point of parabola and y-axis is (0, b); Let f (x) = x2 + 2x + B = 0, from the meaning B ≠ 0 and △ > 0, we can get B ＜ 1 and B ≠ 0. (2) let the general equation of the circle be x2 + Y2 + DX + ey + F = 0, let y = 0 get x2 + DX + F = 0, which is the same equation as x2 + 2x + B = 0, so d = 2, f = B
RELATED INFORMATIONS
- 1. In the plane rectangular coordinate system xoy, let the image of quadratic function f (x) = x ^ 2 + 2x + B have three intersections with the two coordinate axes, and the circle passing through these three intersections is marked as C (I) find the equation of circle C; (II) set point a is a fixed point passed by circle C (its coordinates are independent of B). Ask whether there is a constant k such that the straight line y = KX + K and circle C intersect at points m, N, and | am | = | an |. If it exists, find the value of K; if not, please explain the reason
- 2. In the plane rectangular coordinate system, the distance from the point P (- 3, - 4) to the X axis is () and the distance from the point to the Y axis is
- 3. If the chord length of the straight line 2x-y + 1 = 0 and the section circle x? 2 + y? 2 = R? 2 is equal to 5, find the radius of the circle
- 4. It is known that the distance from point a (2m + 1,3m-5) to the x-axis is twice the distance from the point to the y-axis
- 5. It is known that m (x, y) is a set of inequalities where x is greater than or equal to 0, less than or equal to root 2, y is less than or equal to 2, and X is less than or equal to root sign 2Y If point a (root 2,1), then z = vector OM, the maximum value of point multiplication vector OA is
- 6. The function is equal to the root x + 4, and the value range of the independent variable x is
- 7. Given that ⊙ O1 and ⊙ O2 are circumscribed at point a, the radius of ⊙ O1 is r = 2, and the radius of ⊙ O2 is r = 1, then the circle with radius 4 has () A. 2 B. Four C. Five D. 6
- 8. Given that the length of a chord is equal to the radius r, find: (1) The length of the inferior arc to which the string is directed; (2) The area of the bow formed by this chord and minor arc
- 9. In a rectangular coordinate system, a point whose abscissa and ordinate are integers is called a lattice point. Given that the center of a circle is at the origin and its radius is equal to 5, then the grid point on the circle has______ One
- 10. As shown in the figure, in the plane rectangular coordinate system, the coordinates of the three vertices of △ ABC are a (2, 3), B (2, 1), C (3, 2) (1) Judge the shape of △ ABC; (2) If △ ABC is rotated one circle along the line of edge AC, the volume of the rotating body is obtained
- 11. How to deal with such problems as how many times the radius of a circle, how many times its diameter, how many times its circumference and how many times its area? I will have the final exam tomorrow. Is there any formula?
- 12. When the radius of a circle is several centimeters, its circumference and area are equal
- 13. As shown in the figure, it is known that AB is the diameter of ⊙ o, AC is the chord, and bisection ⊥ bad, ad ⊥ CD, and the perpendicular foot is d Proof: CD is tangent of ⊙ o
- 14. As shown in the figure, in △ ABC, D is a point on AC, e is a point on CB extension line, and AC BC＝EF DF， Confirmation: ad = EB
- 15. As shown in the figure, the straight line DF intersects with AB and AC on both sides of △ ABC at two points D and e respectively, and intersects with the extension line of BC at point F, ∠ B = 50 °, 1 = 76 °, f = 3
- 16. In the RT triangle ABC, the angle ABC = 90 degrees, the circle O with the diameter of AB intersects AC with D, and the tangent passing through D intersects BC with e. it is proved that de = 1 / 2 BC, If Tan angle c = root 5 divided by 2, de = 2, find ad
- 17. As shown in the figure, it is known that AB is the chord of ⊙ o, the radius OA = 20cm, ∠ AOB = 120 ° and the area of ⊙ AOB is obtained
- 18. As shown in the figure, the diameter of ⊙ o is ab = 10, C and D are two points on the circle, and AC＝ CD＝ Let the tangent ed of point d cross the extension line of AC at point F. connect OC to ad at point G (1) Confirmation: DF ⊥ AF (2) Seek the length of OG
- 19. It is known that, as shown in the following four graphs, circle O1 and circle O2 intersect at two points a and B, the line CD passing through point a intersects with circle O1 at C, intersects with circle O2 at D, and straight line ef? 2 passing through point B As shown in the following figure, circle O1 and circle O2 intersect at two points a and B, the line CD passing through point a intersects with circle O1 at C, and with circle O2 at D. the line EF passing through point B intersects with circle O1 at e and circle 02 at F, so as to verify CE ∥ DF Picture in space photo album
- 20. Given that AB and CD are two diameters of circle O, chord CE / / AB, angle COE = 50 degrees, then the acute angle DOB =?