There are () A. 1 B. 2 C. Three D. Four

From the equation of the circle, the coordinates a of the center of the circle are (3,3), and the radius AE is 3,
Then the distance from the center of the circle (3, 3) to the line 3x + 4y-11 = 0 is d = | 3 × 3 + 4 × 3 − 11|
5 = 2, that is ad = 2,
 ed = 1, that is, the distance between E on the circumference and the known straight line is 1, and the existence of P and Q also satisfies the question,
There are three points with a distance of 1 from the point on the circle to the line 3x + 4y-11 = 0
Therefore, C

There are () A. 1 B. 2 C. Three D. Four

If circle C is tangent to the line l1:3x-4y-18 = 0, the shortest distance between the point on circle C and the line l2:3x-4y-3 = 0 is equal to 1, (1) Verification: the center of circle C is on a fixed line (2) If the line L3: x-y-3 = 0 intersects with circle C, the chord length obtained is equal to the root sign 2, then find the standard equation of circle C

If the shortest distance between a circle and a straight line 3x-4y-3 = 0 is 1, then the circle and the straight line are separated, that is, the distance from the center of the circle to the straight line is R + 1, and the radius of the circle is the distance from the center of the circle to the line 3x-4y-18 = 0
1. Let the coordinates of the center of a circle be m (x, y), then | 3x-4y-18 / 5 + 1 = | 3x-4y-3 / 5, which is simplified as 3x-4y-13 = 0;
2. Because the center of the circle is on the line 3x-4y-13 = 0, and the circle is tangent to the line 3x-4y-18 = 0, then the radius of the circle is the distance between the two parallel lines, so r = 1, and the chord length of the intersection between the circle and the line x-y-3 = 0 is the root sign 2, and the distance from the center of the circle to the line x-y-3 = 0 is the root of 2, It is found that the center of the circle is (3, - 1) or (- 5, - 7), so the standard equation of the circle is (x-3) 2 + (y + 1) 2 = 1 or (x + 5) 2 + (y + 7) 2 = 1

In the plane rectangular coordinate system, the line y = - 4 / 3x + 4 1) Find the coordinates of two points (2) Let p be a moving point on line AB (point P does not coincide with point a), let ⊙ P always be tangent to x-axis, and intersect with line AB at two points c and D (the abscissa of point C is less than that of point d). Let the abscissa of point p be m, and the abscissa of point C can be expressed by algebraic formula containing M; (3) Under the condition of (2), if the point C is on the segment AB, what is the value of M, is Δ BOC an isosceles triangle? Secondly, I asked for 1.8m-1.2, - 2.4m + 28 / 15,

M-4.4 / M) = 3m-4.4
If BOC is an isosceles triangle, OC = BC, then the abscissa of point C is half of the length of ob, i.e. 3 / 2
M = 13 / 6
Remember to give points

As shown in Fig. 3, there are two straight lines y = (3 / 4) x + 3 and y = - 3x + 3 in the plane rectangular coordinate system, if the distance between a point m on the line y = - 3x + 3 and the line y = (3 / 4) + 3 The distance is 3 / 2. Try to find the coordinates of point M

Let m (x0, Y0): 0
3/2=|3x0-4(-3x0+3)+12|/√(3^2+4^2)
15/2=|15x0|
x0=±1/2,y0=3±3/2
So m (- 1 / 2,9 / 2) and m (1 / 2,3 / 2) are the coordinates of the points

The straight line y = - 4 / 3x + 4 and X, Y axes intersect at point a and B respectively. In the plane rectangular coordinate system, the distance between the two points a and B and the line a is 2, then the number of lines a satisfying the condition is ()

A(3,0)
B(0,4)
Then AB = 5
Obviously, there are two parallel AB with a distance of 2
If there is a straight line between a and B
Because AB = 5 > 2 times
So there is no such line
So there are only two

As shown in the figure, in the plane rectangular coordinate system, the straight line y = - 4 / 3x + 6 intersects the x-axis and y-axis at two points c and a respectively. Rotate the ray am clockwise about point a for 45 ° to obtain the ray an. Point D is a moving point on am, and point B is a moving point on an. Point C is inside ∠ man 1. Find the length of line AC 2. When am is parallel to the x-axis and the quadrilateral abcabcd is isosceles trapezoid, calculate the coordinates of D 3. If there are points B and D in Fig. 1 to minimize the circumference of △ BCD, then the minimum value is?

Let AB = x, OB = √ 3x, so the coordinates of point a are (√ 3x, x) (1) if ∠ ofd = 90 ° of = ob, then the coordinates of point D are (x, √ 3x) substituting y = x? To get x = √ 3 〈 the coordinates of point a are (3, √ 3) (2) if ∠ ofd = 90 ° of = AB, then the coordinates of point D are (√ 3x, x) are replaced by y = x? To get x = 1 /

As shown in the figure, in the plane rectangular coordinate system, the straight line L passes through point a (2, - 3), intersects with X axis at point B, and with the straight line y = 3x − 8 3 parallel (1) Find: the function analytic formula of line L and the coordinates of point B; (2) If there is a point m (a, - 6) on the straight line L, then make the perpendicular line of X axis through the point m, and the intersection line y = 3x − 8 3 at point n, find a point P on line Mn so that △ PAB is a right triangle and ask for the coordinates of point P

(1) Let the analytic formula of the line l be y = KX + B (K ≠ 0), ∵ the line L is parallel to y = 3x-83,

In the plane rectangular coordinate system, the straight line y = - 4 / 3x + 4 intersects X axis and Y axis respectively at point a, B, and point C (0, n) is the point coordinate plane on the Y axis Fold along the line AC so that point B just falls on the X axis. What is the coordinate of point C

Make CD ⊥ AB in D through C, as shown in Fig,
For the straight line y = - 3 / 4x + 3, if x = 0, y = 3; if y = 0, x = 4,
A (4,0), B (0,3), that is, OA = 4, OB = 3,
∴AB=5,
And ∵ the coordinate plane is folded along the line AC so that point B just falls on the x-axis,
Ψ AC bisection ∠ OAB,
If CD = co = n, then BC = 3-N,
∴DA=OA=4,
∴DB=5-4=1,
In RT △ BCD, DC2 + BD2 = BC2, ν N2 + 12 = (3-N) 2, the coordinate of point C is (0,4,3)

There are () A. 1 B. 2 C. Three D. Four