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The radius of a circle is 5cm, and the arc length opposite a central angle is 6.28cm______ Degree
According to the arc length formula L = n π R180, the center angle of the sector is: 6.28 △ 3.14 △ 5 × 180, = 0.4 × 180, = 72 (degrees). Answer: the center angle of the sector is 72 degrees, so the answer is: 72
The equation of the smallest circle whose center is on the curve y = 3x (x > 0) and tangent to the straight line 3x + 4Y + 3 = 0 is______ ．
Let the center of the circle be (a, 3a), a > 0, and the shortest distance from the center of the circle to the straight line be: | 3A + 4 × 3a | + 39 + 16 = 15 | 3A + 12a + 3 | = R | 3A + 12a + 3 | = 5R ∵ a > 0, | 3A + 12a + 3 = 5R. The equation for finding the minimum area of the circle is to find the value of a and R, 5R = 3A + 12a + 3 ≥ 23a · 12a + 3 = 15 | R ≥ 3. When 3A = 12a, i.e. a = 2, take the equal sign, the radius of the circle with the smallest area is r = 3, and the center of the circle is (2, 32) The equation of the smallest circle is: (X-2) 2 + (y-32) 2 = 9
The equation for finding a circle whose center is at point C (3, - 2) and tangent to the line 3x-4y-7 = 0
Find the radius of the circle first
From the formula of distance from point to line
r=[3*3-（-2）*4-7]/5=2
So the equation is:
(x-3)^2+(y+2)^2=4
The equation of a circle with point (2-1) as its center and tangent to the line 3x-4y + 5 = 0 is?
Radius of circle r = D = ┃ 3 * 2-4 * (- 1) + 5 ┃ / √ (3 ^ 2 + (- 4) ^ 2) = 3
The equation of circle is: (X-2) ^ 2 + (y + 1) ^ 2 = 3 ^ 2 = 9
Finding the equation of the line x-y-2 = 0 symmetric to the line 3x-y + 3 = 0
Y = 5x + 8 is wrong!
The answer is y = - 7x + 22
y=-7x+22
The slope is - 7
Calculation method:
(k-3)/(1+3k)=(3-1)/(1-3*1)=>k=-7
The intersection is (- 5 / 2, - 9 / 2)
x-y-2=0
{= > intersection coordinates
3x-y+3=0
Let y = - 7x + B and substitute the intersection point to solve B = 22
Given the line L: y = x + 3. (1) find the equation of the line L with respect to the line symmetrical at point M. (2) find the equation of the line x-y-2 with respect to the line symmetrical at point L
L:y=x+3
(1)
M(a,b)
L^(x,y)
xL+xL^=2a,xL=2a-xL^=2a-x
yL+yL^=2b,yL=2b-yL^=2b-y
yL=xL+3
2b-y=2a-x+3
y=x+2b-2a-3
(2)
x-y-2=0
y=x-2
3-(-2)=5=8-3
y=x+8
The linear equation of 3x-y + 3 = 0 with respect to x-y-2 = 0 symmetry is______ ．
Because the slope of the straight line x-y-2 = 0 is 1, there is x = y + 2Y = x − 2. Substituting it into the straight line 3x-y + 3 = 0, we get 3 (y + 2) - (X-2) + 3 = 0. Sorting out, we get x-3y-11 = 0. So the answer is: x-3y-11 = 0
Given the line I: y = 3x + 3, the equation of the line x-y-2 = 0 with respect to the l-symmetric line is obtained
From x-y-2 = 0 and 3x-y + 3 = 0, x = - 5 / 2, y = - 9 / 2
Then three straight lines intersect at the point: (- 5 / 2, - 9 / 2)
Let the linear equation be y + 9 / 2 = K (x + 5 / 2)
The angle from the straight line x-y-2 = 0 to the straight line 3x-y + 3 = 0 is equal to the angle from the straight line 3x-y + 3 = 0 to the straight line
(3-1)/(1+3),=(K-3)/(1+3k)
So, k = - 7
So the linear equation is: 7x + y + 22 = 0
Why is the angle from the straight line x-y-2 = 0 to the straight line 3x-y + 3 = 0 equal to the angle from the straight line 3x-y + 3 = 0 to the straight line
How does the formula (3-1) / (1 + 3), = (K-3) / (1 + 3K) come from,
If x-y-2 = 0 and 3x-y + 3 = 0, x = - 5 / 2, y = - 9 / 2, then the three straight lines intersect at the point d (- 5 / 2, - 9 / 2)
The linear equation of point a (2,0) passing through point a perpendicular to y = 3x + 3 is y = - 1 / 3 (X-2). By y = - 1 / 3 (X-2) and y = 3x + 3, the intersection point B (- 7 / 10,9 / 10) of two lines can be obtained. The symmetric point C (- 17 / 5,9 / 5) of point a about point B can be obtained. The linear equation 7x + y + 22 = 0 can be obtained from C and D (you can understand it with the help of figures)
,
The equation ()
A.(x-4)²+(y-2)²=20
B.(x+4)²+(y-2)²=20
C.(x-4)²+(y+2)²=20
D.(x+4)²+(y+2)²=20
[find the center of the circle first]
The midpoint of AB is (- 1,1), and the slope of AB is k = (2-0) / (- 2-0) = - 1
So the slope of the perpendicular of AB is k = 1
So the perpendicular of AB is Y-1 = 1 * (x + 1)
That is y = x + 2
Then the center of the circle is the intersection of the perpendicular of AB and the straight line x-2y = 0
To solve the equations {y = x + 2, x-2y = 0, the center of the circle is (- 4, - 2)
[find the radius again]
r=√[(-4-0)²+(-2-0)²]=2√5
So the equation of circle is (x + 4) &# 178; + (y + 2) &# 178; = 20
So choose D
If you don't understand, please hi me, I wish you a happy study!
The equation for finding a circle passes through two points a (- 1,0) B (3,2), and the center of the circle is on the line x + 2Y = 0
The slope of AB is 0.5
So the slope of the vertical in AB is - 2
So the equation of the middle perpendicular is as follows:
y-1=-2(x-1)
That is: 2x + Y-3 = 0
Simultaneous: x + 2Y = 0
x=2
y=-1
So the center of the circle is (2, - 1)
r^2=3^2+1^2=10
The circular equation is as follows:
(x-2)^2+(y+1)^2=10
PS: calculate the center of a circle by crossing the center of the circle with the middle perpendicular of the string
RELATED INFORMATIONS
- 1. If the length of an arc is 12 π cm and the center angle of the arc is 108 °, the radius of the arc is
- 2. The length of an arc is 31.4, the radius of the circle is 30, then the central angle of the arc is () degrees
- 3. There is a moving point a on the number axis. It starts from the origin and moves along the number axis. It is only allowed to move one unit at a time. After 10 times of movement, point a moves to 6 points away from the origin Unit, how many ways does point a move
- 4. The point representing the number a on the number axis must be to the right of the origin Judge right or wrong
- 5. On the number axis, the origin indicates whether the starting point is right or wrong
- 6. On the number axis, a point 5 units from the origin represents the number______ The absolute value is the number of itself______ ．
- 7. The point of - 3 on the number axis is marked as a, the point of 2 is marked as B, and the point of a is marked as a______ Edge movement______ The distance between a and B is______ ．
- 8. A is the point of negative one on the number axis. Move a to the left two unit lengths along the number axis to reach B, then the number represented by B is
- 9. It is known that the perimeter of the sector is 20 cm and the area is 16 square cm. The radius of the sector is calculated
- 10. The perimeter of a rectangle is 72 meters. If its width increases by 1 / 4 and its length decreases by 1 / 8, and its perimeter remains the same as the original, what is the area of the rectangle?
- 11. The arc length and area of a sector are both 5, and the arc number of the central angle of the sector is 5______ ．
- 12. The arc length and area of a sector are both 5. Find the degree of the central angle of the sector
- 13. The arc length and area of a sector are both 5, and the arc number of the central angle of the sector is 5______ ．
- 14. If the radius of the sector is 30 and the center angle is 60 degrees, the area of the sector is
- 15. Cut a circle and a sector from the square sheet iron to form a cone (as shown in the figure). If the radius of the circle is R and the radius of the sector is r, then the radius of the circle accounts for half of the radius of the sector______ %．
- 16. On the square sheet iron with the side length of 46 cm, cut a circular sheet iron and a fan-shaped sheet iron as shown in the figure, just to make a cone model, then the bottom radius of the cone model is______ Cm
- 17. The radius of a circle is 5cm, the degree of sector is 60, and what is the sector area
- 18. If a circle is inscribed on a sector with a central angle of π / 3 and a radius of R, the ratio of the area of the circle to the sector is_____ .
- 19. If the sector area is 37.68 square centimeters and the radius of the circle is 6 centimeters, how long is the sector arc? How many degrees is the center angle?
- 20. Find the value of √ (1996 * 1997 * 1998 * 1999 + 1)