As shown in the figure, in the plane rectangular coordinate system, the straight line L: y = - 2x-8 intersects with the x-axis and y-axis respectively at two points a and B. the point P (0, K) is a moving point on the negative half axis of the y-axis. Take P as the center of the circle and 3 as the radius to make ⊙ P Q: when what is the value of K, ⊙ P is tangent to the line L

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• 1. In the plane rectangular coordinate system, the line y = - 2x-8 intersects the X axis and Y axis at a and B respectively, and the point P (0, K) is a moving point on the negative half axis of Y axis Take P as the center of the circle and 3 as the radius to make the circle P, (1) connect PA, if PA = Pb, try to judge the position relationship between the circle P and the X axis, (2) under the condition of (1), find the analytical formula of the straight line AP. (3) under the conditions of (1) and (2), point G is a point on the straight line AB, through point G do GH ⊥ X axis intersection straight line AP at point h, ask whether there is a point G, Let P, O, G, h as the vertex of the quadrilateral for parallelogram. If there is to find the coordinates of point G, if not, explain the reason
• 2. In the plane rectangular coordinate system, there are two straight lines, y = 3 / 5x + 9 / 5 and y = - 3 / 2x + 6. Their intersection point is m. The first line intersects with X axis at point a, and the second line intersects with X axis at point a Intersection with X axis at point B (1) Find the coordinates of two points a and B; (2) Using the image method to solve the equations; {3x-5y = - 93x + 2Y = 12 (3) Find the area of △ mAb)
• 3. In the rectangular coordinate system as shown in the figure, a and B are two points on the x-axis, and the circle with ab as the diameter intersects the y-axis at C. suppose that the analytical formula of the parabola passing through a, B and C is y = xx-mx + N, and the sum of the two reciprocal of the equation xx-mx + n = 0 is - 2 (1) Find the value of n (2) Find the analytical formula of this parabola (3) Let a straight line parallel to the x-axis intersect the parabola at two points E and F. ask if there is a circle with the diameter of line segments E and f just tangent to the x-axis? If so, find out the radius of the circle; if not, explain the reason
• 4. As shown in the figure, if a circle is tangent to the x-axis in the plane rectangular coordinate system at point a (8,0), and intersects with the y-axis at points B (0,4), C (0,16), then the diameter of the circle is______ ．
• 5. As shown in the figure, in the plane rectangular coordinate system xoy, the circle e with a diameter of 10 intersects the x-axis at points a and B, and intersects the y-axis at points c and D. the coordinates of points a and B are as follows: A (- 2,0), B (4,0). Try to find the coordinates of center E and points c, D Thank you）
• 6. The standard equation of the circle whose center is on the line y = - 2x and passes through the point a (0,1) and is tangent to the line x + y = 1
• 7. Let the circle pass through point a (2, - 3), the center of the circle be on the straight line 2x + y = 0, and tangent to the straight line x-y-1 = 0, then the standard equation of the circle can be solved
• 8. The standard equation of a circle whose center is on 2x-y = 3 and tangent to two coordinate axes Two equations
• 9. Find the standard equation of the circle whose center is on the line 2x-y-3 = 0 and tangent to the X axis at the point (- 2,0) The standard equation of the circle whose center is on the line 2x-y-3 = 0 and tangent to the x-axis at the point (- 2,0)
• 10. It is known that the center of circle C is on the straight line 2x-y-3 = 0, and the standard equation of circle C can be obtained through points a (5,2), B (3,2)
• 11. As shown in the figure, in the plane rectangular coordinate system, the analytical expression of the straight line L is y = - 2x-8, L respectively intersects at two points a and B on the x-axis and y-axis, and the point P (0, K) is a moving point on the negative half axis of the y-axis. Take P as the center of the circle and 3 as the radius to make the circle P 2) When k is the value, the triangle with the two intersections of circle P and line L and the center of circle P as the vertex is an equilateral triangle? Come on, it's urgent,
• 12. In the plane rectangular coordinate system, the line y = KX + B intersects with the negative half axis of X axis at point a, and the positive half axis of Y axis at point B. the circle P passes through points a and B (the center P of the circle is on the negative half axis of X axis). It is known that ab = 10, AP = 25 / 4 1) The analytic formula of the straight line y = KX + B 2) Is there a point Q on the circle P such that the quadrilateral with apbq as its vertex is a diamond? If it exists, request the coordinates of point Q
• 13. If the difference between the algebraic formula 18 + m / 3 and M - 2 / 5 is 8, find the value of M and remove the denominator
• 14. When m is the value, the value of the algebraic formula 3 (m-2) 2 + 1 is 2 times larger than that of 2m + 1?
• 15. Given m ^ 2 + M-1 = 0, find the value of the algebraic formula m ^ 3 + 2m ^ 2 + 2004
• 16. The line L passes through point P (2,1) and intersects with the positive half axis of X axis and Y axis at two points a and B respectively. O is the origin. When the perimeter of triangle OAB is the minimum, the equation of line L is obtained
• 17. Let the circle (X-2) ^ 2y-3) ^ 2 = 1, a point P (x0, Y0) and a point P (x0, Y0). The tangent to the circle is m, O is the origin of the coordinates, and | PM | = | Po |
• 18. Draw a point P (x0, Y0) from the circle C: x ^ 2 + y ^ 2-2x-2y-2 = 0 to the tangent line of the circle, the tangent point is m, O is the coordinate origin, and | PM | = | Po | Draw a point P (x0, Y0) from the circle C: x ^ 2 + y ^ 2-2x-2y-2 = 0 to the tangent line of the circle, the tangent point is m, O is the coordinate origin, and | PM | = | Po |, find the minimum P point coordinate of | PM |
• 19. Make a circle (x + 1) ^ 2 + (Y-2) ^ 2 = 1 tangent through point P, and the tangent point is m. if the length of PM = the length of Po, then the minimum value of PM
• 20. It is known that P is an arbitrary point on the image with inverse scale function y = K / X (k > 0). Through P, make a vertical line of X axis, and the perpendicular foot is m. It is known that s △ POM = 2 (1) Finding the value of K (2) If the image of the line y = x and the inverse scale function intersects with point a in the first quadrant, the analytic expression of the line passing through point a and point B (0, - 2) is obtained Well, I don't know how to insert illustrations