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It is known that the center of circle m is on the straight line 2x-y + 5 = 0 and intersects with y axis at two points a (0, - 2), B (0,4) (1) to solve the equation of circle M (2) Find the tangent equation of circle m passing through point C (- 4,4); (3) given D (1,3), point P moves on circle m, find the trajectory equation of vertex Q of parallelogram adqp with AD and AP as a group of adjacent sides
1) Because the circle intersects with the Y axis at a and B, the center of the circle is on the vertical bisector of AB, that is, the ordinate of the center is (- 2 + 4) / 2 = 1, in 2x-y + 5 = 0, let y = 1 get x = - 2, so the center of the circle is m (- 2,1), R ^ 2 = ma ^ 2 = (- 2-0) ^ 2 + (1 + 2) ^ 2 = 13, so the equation of the circle m is (x + 2) ^ 2 + (Y-1) ^ 2 = 13.2
If the intersection of circle C and Y axis on the straight line 2x-y-7 = 0 and two points a (0, - 4), B (0, - 2), then the equation of circle C is
Find the center of the radius
Let the center of the circle be (a, 2a-7)
The equation is: (x-a) ^ 2 + (y-2a + 7) ^ 2 = R ^ 2
Substituting a and B, we can get the following results respectively
a^2+(3-2a)^2=r^2
a^2+(5-2a)^2=r^2
By subtracting the two formulas: - 16 + 8A = 0
That is, a = 2
That is, R ^ 2 = 2 ^ 2 + (3-4) ^ 2 = 5
So the equation is: (X-2) ^ 2 + (y + 3) ^ 2 = 5
RELATED INFORMATIONS
- 1. It is known that the circle C and the y-axis intersect at two points m (0, - 2), n (0, 2), and the center of the circle C is on the straight line 2x-y-6 = 0. (1) find the equation of the circle C; (2) make a straight line through the center of the circle C, so that the line AB sandwiched between two straight lines l1:2x-y-2 = 0 and L2: x + y + 3 = 0 is exactly bisected by the point C, and find the equation of the straight line
- 2. The Y-axis of the circle center on 2x-y-7 = intersects at (0, - 4), (0, - 2), and the circle equation is solved
- 3. It is known that the center of circle C is on the straight line 2x-y-3 = 0 and passes through points a (5,2), B (3,2) Find 1. The chord length of line L passing through point P (2,1) and intersecting circle C is 2 root sign 6. Find the equation of line L 2. Let Q be the moving point on the circle C and o be the origin of the coordinate, and try to find the maximum area of OPQ of the triangle
- 4. Given that point P is a moving point on circle C: x ^ 2 + y ^ 2 + 2x = 0, a (1,0), and that the vertical line of line PA intersects the straight line PC at point m, then the trajectory equation of point m is
- 5. The equation of the circle whose center is on the line 2x + y = 0 and tangent to the point (2, - 1) with the line x + Y-1 = 0 is______ ．
- 6. AD.BC Is the chord of two short points of diameter AB passing through the circle, and BD and AC intersect at point e. it is proved that AC × AE + BD × be = AB ^ 2
- 7. If the line L and the line y = 2x-1 are symmetric about the X axis, find the functional relation of the line L and solve it by the method of function
- 8. How to make triangles in the Geometer's Sketchpad? Move ABC to a'b'c ', and then move ABC back from a'b'c'. Control the two movements separately
- 9. Is the definite integral of inverse proportional function from 0 to 1 positive infinity? Why does the Geometer's Sketchpad show 11 / 3 of the answer?
- 10. Draw a vertical line from a vertex of a triangle to the line of its opposite side. What is the line between the vertex and? The line segment is called the height of the triangle. At what point do the three heights of the triangle intersect?
- 11. As shown in the figure, in RT △ AOB, the circle AB with radius OA intersects at point C. If Ao = 5, OB = 12, the length of BC is obtained
- 12. As shown in the figure, ∠ AOB = 30 °, OC bisects ∠ AOB, CD ⊥ OA in D, CE ∥ Ao intersects ob in E & nbsp; & nbsp; OE = 20cm, calculate the length of CD
- 13. In the circle O, the radius is 4 and the angle AOB is 60 degrees. Point C is the midpoint of arc AB, CM is vertical OA, CN is vertical ob, and the perpendicular feet are points m and N, respectively (1) (2) when point C moves on arc AB, try to judge whether the length of Mn changes and prove your conclusion (1) (2) when point C moves on arc AB, try to judge whether the length of Mn changes and prove your conclusion
- 14. OA is the radius of circle O, OP is perpendicular to OA, the chord AB intersects op with C, and Pb = PC
- 15. As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E
- 16. As shown in the figure, in the two concentric circles with o as the center, the chord AB and CD of the big circle are equal, and AB and the small circle are tangent at point E
- 17. The radius of two concentric circles, the radius of the big circle, the opposite extension lines of OA and ob intersect the small circle at C and D respectively. It is proved that AB is parallel to CD
- 18. In RT △ ABC, ∠ C = 90 °, ab = 5, BC = 4, find the radius of inscribed circle______ ．
- 19. As shown in the figure, a, B, C and D are the four points on the circle O, and the verification of AC / / BD, OA ⊥ ob is ad ⊥ BC
- 20. As shown in the figure, in the circle O with radius r, the angle AOB is equal to 2a, and OC is perpendicular to ab at point C. find the length of the chord AB and the distance between the chord centers