(2010` Guangzhou the first mock exam) the known moving circle C passes through point A (-2,0) and is cut in with the circle M: (X-2) ^2+y^2=64. (1) Find the trajectory equation of the center of moving circle C (2) Let L: y = KX + m (where k, m ∈ z) and (1) intersect at two different points B and D, and hyperbola (x ^ 2) / 4 - (y ^ 2) / 12 = 1 intersect at two different points e F. ask if there is a straight line L such that vector DF (vector) + be (vector) = 0 (vector). If there are, please point out how many such lines. If not, please explain the reason

(2010` Guangzhou the first mock exam) the known moving circle C passes through point A (-2,0) and is cut in with the circle M: (X-2) ^2+y^2=64. (1) Find the trajectory equation of the center of moving circle C (2) Let L: y = KX + m (where k, m ∈ z) and (1) intersect at two different points B and D, and hyperbola (x ^ 2) / 4 - (y ^ 2) / 12 = 1 intersect at two different points e F. ask if there is a straight line L such that vector DF (vector) + be (vector) = 0 (vector). If there are, please point out how many such lines. If not, please explain the reason

(1) A in the circle m (2) the second question you ask is simultaneous equations, using Weida's theorem, but note
Therefore, the discriminant of the difference equation that the circular contraction distance of circle C and circle m is equal to the radius of two circles
Let C be the center of a circle (x, y)
√[(x-2)^2+y^2]=8-√[(x+2)^2+y^2]
Transfer of items
√[(x-2)^2+y^2]+√[(x+2)^2+y^2]=8
According to the definition of ellipse, the equation is
x^2/16+y^2/12=1

Find the equation with radius of root 5 and tangent to point P (3,1) with straight line x-2y-1 = 0

If the center of the circle is on the x-axis, the circle C with radius of 5 is on the left side of the Y-axis and is tangent to the line x + 2Y = 0, then the standard equation of circle C is______ ．

The center of a circle on the x-axis is (a, 0), r = 5, the distance from the center to the tangent x + 2Y = 0 is equal to the radius, so | a + 0 | 12 + 22 = 5, and | a | 5 is on the left side of the y-axis, then a < 0, so a = - 5. The standard equation of circle C is: (x + 5) 2 + y2 = 5. So the answer is: (x + 5) 2 + y2 = 5

If the center of the circle is on the x-axis, the circle O with radius 5 is on the left side of the Y-axis and tangent to the line x + 2Y = 0, then the equation of the circle O is ()
A. (x−5)2+y2＝5B. (x+5)2+y2＝5C. （x-5）2+y2=5D. （x+5）2+y2=5

Let the coordinates of the center of the circle be (a, 0), then the equation of the circle is (x-a) 2 + y2 = 5 (a < 0). According to the distance from the center of the circle to the straight line x + 2Y = 0 equal to 5, that is | a + 0 | 5 = 5, the solution is a = - 5, a = 5 (rounding off), then the equation of the circle is: (x + 5) 2 + y2 = 5