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It is known that the equation of circle C is x2 + y2-6x-2y + 5 = 0. The moving line L passing through point P (2,0) intersects with circle C at two points P1 and P2. Let P1 and P2 be tangent lines L1 and L2 of circle C respectively. Let the intersection of L1 and L2 be m. prove that point m is on a fixed line, and work out the equation of this fixed line
The center of C: (x-3) 2 + (Y-1) 2 = 5 is (3, 1) Let P1 (x1, Y1), P2 (X2, Y2), m (x0, Y0) Because p1m is tangent to circle C, MP1 ⊥ CP1 (4 points) so (x1-x0) (x1-3) + (y1-y0) (y1-1) = 0
RELATED INFORMATIONS
- 1. It is known that the distances from P1 (a-1,5), P2 (2, B-1) to X-axis are equal, and p1p2 is parallel to Y-axis to calculate the value of (a + b) to the power of 2012
- 2. Given P1 (2,5, - 6), find a point P2 on the Y axis so that | p1p2 | = 7
- 3. If the points P1 (- 1,3) and P2 (1, b) are known, and p1p2 is parallel to the X axis, then B =?
- 4. Given that a line L is parallel to the X axis, P1 (- 2,3) P2 (X2, Y2) is two points on the line L, and the distance between P1 and P2 is 4, then the coordinate of P2 is
- 5. According to the following conditions, find the distance P1 (0, - 2) P2 (3,0) p1 (- 3,1), P2 (2,4) p1 (4, - 2) P2 (1,2)
- 6. The expression of L1 and L2 is y = 3 / 4x + 3, y = 3 / 4x-3, then the distance between these two parallel lines is
- 7. If two straight lines ax-by + 4 = 0 and (A-1) x + y + B = 0 are parallel and the distance from the origin of the coordinate to the two straight lines is equal, find the straightness of a and B
- 8. If line L1: ax by + 4 = 0 and line L2: (A-1) x + y + B = 0 are parallel and the distance between the two lines at the origin is equal, find a and B Doesn't that mean the two lines coincide? I'm a / (A-1) = - B / 1 = 4 / b I see, but why can't I work out the answer by using the distance equality formula
- 9. If the moving points a (x1, Y1) and B (X2, Y2) move on the line L1: x + Y-7 = 0 and L2: x + Y-5 = 0 respectively, the minimum distance from the midpoint m of line AB to the origin is () A. 23B. 33C. 32D. 42
- 10. It is known that two straight lines L1: ax by + 4 = 0, L2: (A-1) x + y + B = 0. The line L1 is parallel to L2, and the distance from the origin of the coordinate to L1 and L2 is equal. The value of a and B can be obtained
- 11. Given two points P1 (- 3,5) P2 (5, - 7), the equation of vertical bisector of line p1p2 is obtained Urgent need
- 12. The distance from point P (a, 3) to the line 4x-3y + 1 = 0 is equal to 4, and the inequality is 2x = y
- 13. Given that P is a point on the line 4x-y-1 = 0, the distance from P to the line 2x + y + 5 = 0 is equal to the distance from the origin to the line, then the coordinate of P is?
- 14. Given that the point P is on the straight line y = 2x + 3, and the distance from the point P to the origin is equal to twice the distance from the point P to the y-axis, find the coordinates of the point P
- 15. Point m is on the line y = 2x. If the distance from m to the origin is equal to the distance from m to the line x-2y + 8 = 0, find the coordinates of point M
- 16. If there are only two points on the circle C: (x-3) ^ 2 + (y + 5) ^ 2 = R ^ 2 and the distance from the two points to the straight line L: 4x-3y = 17 is 1, what is the value range of R?
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- 18. Let (x + 3) square (y + 5) square = R square have and only have one point, and the distance from the line 4x-3y + 2 = 0 is equal to 1, then the radius of the circle R is ()
- 19. If the distance from point P (a, 3) to the line 4x-3y + 1 = 0 is equal to 4 and in the plane region represented by the inequality 2x + Y-3 < 0, then the coordinates of point P are______ ．
- 20. The distance from point P (- 2,1) to line 4x-3y + 1 = 0 is equal to?