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The common chord length of circle x2 + y2-4 = 0 and circle x2 + y2-4x + 4y-12 = 0 is () A. Two B. Three C. 2 Two D. 3 Two
By subtracting the equation of circle x2 + y2-4 = 0 and circle x2 + y2-4x + 4y-12 = 0, X-Y + 2 = 0,
∵ the distance from the center of the circle (0, 0) to the straight line X-Y + 2 = 0 d = 2
2=
2，r=2，
Then the common chord length is 2
r2−d2=2
2．
Therefore, C is selected
The common chord length of circle x2 + y2-4 = 0 and circle x2 + y2-4x + 4y-12 = 0 is () A. Two B. Three C. 2 Two D. 3 Two
0
0
Given that the circle x2 + y2-4x + 4Y + 6 = 0, the center of the circle is (2, - 2), and the radius is
2．
The center of the circle is (2, - 2) to the straight line x-y-5 = 0
Two
2．
Using geometric properties, the chord length is 2
(
2)2−(
Two
2)2=
6．
Therefore, a
Two circles x2 + y2-2x + 4Y + 4 = 0 and X2 + y2-4x + 2Y + 19 The positional relation of 4 = 0 is () A. Tangency B. Intersection C. Contains D. Exotropism
The circle x2 + y2-2x + 4Y + 4 = 0, i.e. (x-1) 2 + (y + 2) 2 = 1, represents a circle with m (1, - 2) as its center and radius equal to 1
Trajectory equation of a point P (1, - 1) in ellipse x ^ 2 + 4Y ^ 2 = 16 Let a (x1, Y1) B (X2, Y2) AB midpoint (x0, Y0) let x0 not be 1 Let the straight line passing through p be y = K (x-1) - 1 Then Y0 = K (x0-1) - 1. K = (Y0 + 1) / (x0-1) Replace AB into the ellipse x1^2+4y1^2=16 x2^2+4y2^2=16 By subtracting the two formulas (x1^2-x2^2)+4(y1^2-y2^2)=0 (x1+x2)(x1-x2)+4(y1+y2)(y1-y2)=0 2x0(x1-x2)+8y0(y1-y2)=0 2. Divide by the same (x1-x2) x0+4y0*k=0 Because k = (Y0 + 1) / (x0-1) So x0 + 4y0 * (Y0 + 1) / (x0-1) = 0 Simplified X ^ 2-x + 4Y ^ 2 + 4Y = 0 (x is not equal to 1) When x = 1, the midpoint (1,0) also conforms to the equation x^2-x+4y^2+4y=0 How did 2x0 (x1-x2) + 8y0 (y1-y2) = 0 come about?
Isn't (x0, Y0) the midpoint of a (x1, Y1) B (X2, Y2) two points? Since it is the midpoint, then there is 2x0 = X1 + X2, 2y0 = Y1 + Y2
Ellipse x2 16+y2 In 9 = 1, the equation of the line where the chord with point m (- 1,2) as the midpoint is______ .
Let the two ends of a chord be a (x1, Y1), B (X2, Y2), substitute the ellipse to get x 1216 + y 129 = 1 x 2216 + y 229 = 1, and subtract the two formulas to get (x1 − x2) (x1 + x2) 16 + (Y1 − Y2) (Y1 + Y2) 9 = 0, and then Y1 − y2x1 − x2 = 932 ﹣ the line where the chord is located is obtained
Let's know the ellipse x ^ 2 / 16 + y ^ 2 / 4 = 1. Introduce a chord through the point P (2,1) so that the string is bisected by this point, and find the equation of the line where the string is located and the chord length
Let P and ellipse intersect at two points a (x1, Y1) B (X2, Y2)
Two point coordinates are introduced into the elliptic equation
x1^2/16+y1^2/4=1
x2^2/16+y2^2/4=1
Subtracting the two formulas, (x1 + x2) (x1-x2) + 4 (Y1 + Y2) (y1-y2) = 0
k=(y1-y2)/(x1-x2)=-(x1+x2)/4(y1+y2)=-2*2/(4*2*1)=-1/2
The point oblique formula of AB equation is Y-1 = - (X-2) / 2
x+2y-4=0
Y = - X / 2 + 2 is introduced into the elliptic equation
2x^2-8x=0
X = 0 or 4
|AB|=√(k^2+1)|x1-x2|=2√5
If a chord passing through a point (2.1) in the ellipse x square / 16 + y square / 4 = 1 is bisected by the point, then the equation of the line where the chord is located is?
The equation of the straight line where the chord is set is y-1=k (X-2) and X square /16+Y square /4=1. The equation of the straight line where the chord is set is y-1=k (X (X-2) and x^2+4 (kx-2k+1) ^2-16=0. Simplify: (4k^2+1) x^2-8k (2k-1) +(2k-1) ^2-16=0, if the sum of the absabsciscoordinates of 2 intersections if the sum of the absabsciscoordinates of 2 intersections if (4k^2+1) x^2-8k (2k-1) +(2k-1) ^2-16=0 =x1+x2=8k (2k-1) / (4k^2+1) point (2.1) is the middle point of 2 intersections if (4k^2+1) x^2-8k (2k-1) +(2k-1) +(2k-1) ^2-16=0, then the sum of the absciscoordinates of 2 intersections =x1+x2=8k (2k-1) / (4k^2+1) point (2.1) is the middle point of 2 intersections if point (8K (2k-1) 8K (2k-1) if point (2.1) is the middle point of 2 intersections if (2k(2k-1 / (4
In ellipse x2 16+y2 In 4 = 1, the linear equation of the chord passing through point m (1, 1) and bisected by this point is () A. x+4y-5=0 B. x-4y-5=0 C. 4x+y-5=0 D. 4x-y-5=0
Let P1 (x1, Y1), P2 (X2, Y2) be the two ends of chord with point m (1, 1) as the midpoint,
Then X1 + x2 = 2, Y1 + y2 = 2
Another x12
16+y12
4=1，①
X22
16+y22
4=1，②
① - 2 obtained: (x1 + x2) (x1-x2)
16+(y1+y2)(y1-y2)
4=0
According to symmetry, x1 ≠ x2,
The slope of the straight line with the chord whose midpoint is point M (1, 1) k=-1
4，
The equation of the line where the midpoint chord is located is Y-1 = - 1
4 (x-1), that is, x + 4y-5 = 0
Therefore, a
In the ellipse x + 4Y = 16, the line equation and chord of the chord which has passed the point m (2,1) and is bisected by this point is located. Thank you,
Let the line equation be Y-1 = K (X-2) and the intersection point of line and ellipse is (x1, Y1) (X2, Y2), then there is X1 + 4Y1 = 16, X2 + 4y2 = 16. Subtracting the two formulas, x1-x2 + 4y1-4y2 = 0 is (x1 + x2) (x1-x2) + 4 (Y1 + Y2) (y1-y2) = 0 (1) because m (2,1) is the midpoint of point (x1, Y1) and point (X2, Y2), then there is (x1 + x2) / 2 = 2
RELATED INFORMATIONS
- 1. If P9 (2, - 1) is the midpoint of the chord ab of the circle (x-1) 2 + y2 = 25, what is the equation of AB
- 2. Finding the minimum area of the intersection of the two circles of the sum of the two Y 2-2x-2x-2y = 0-2x-2
- 3. It is known that the center of circle C is tangent to the line l2:4x + 3Y + 14 = 0 on the line L1: x-y-1 = 0, and the straight line l3:3x + 4Y + 10 = 0 is obtained. The chord length is 6, and the equation of circle C is obtained
- 4. (1) Find the equation of straight line passing through the intersection point of the line l1:7x-8y-1 = 0 and l2:2x + 17Y + 9 = 0 and perpendicular to the line 2x-y + 7 = 0 (2) The straight line L passes through the point P (5, 5) and intersects the circle C: x2 + y2 = 25, and the chord length is 4 5. Find the equation of L
- 5. 0
- 6. Through a point P (2,0) in the ellipse x ^ 2 / 9 + y ^ 2 / 4 = 1, the chord AB is induced and the trajectory equation of the midpoint m of the chord is obtained Thinking
- 7. Given that the straight line passes through the point m (2,1), and the chord length cut by the circle C: (x-1) 2 + (y + 1) 2 = 4, the chord length is 2 √ 2, and the equation of the straight line is obtained
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- 14. The ratio of () to () of a circle is called PI, which is represented by the letter ()
- 15. In order to know that the circumference of a square is equal to that of a circle, the side length of a square is 6.28 cm, and the circumference of the circle is () cm? The area is () square centimeter?
- 16. Draw the largest circle in the square. The circumference of the circle is 12.56 cm. The area of the square is______ .
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- 18. Relating to the PI and the circumference of a circle The circumference of a circle = Pi times d or 2 times R. are these two formulas? Are they used to calculate the circumference? If so, then I understand the first formula It's PI times diameter The second one doesn't understand 2 times the radius? 2 times the radius. I understand. It's the diameter and then the circumference But what does the multiplication radius of the 2-fold school represent? What is the multiplication of two 3.14? What does it represent? In addition, what does the PI represent? What is the relationship between PI and radius, diameter and circumference? Please give an example to illustrate What does circumference apart from diameter represent?
- 19. Within a circle, the ratio of the diameter of a circle to its circumference is called PI Pay attention to the questions. I used to type X on the test paper, but many people check √, so I want to have a look My understanding: "the ratio of the diameter of a circle to the circumference of a circle" is wrong. It should be "the circumference of a circle and the diameter of a circle"! Thank you for helping me to answer the friend!
- 20. Who has the PI accurate to 1 to 100?