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The equation of circle C is known as x ^ 2 + y ^ 2-6c-8y + 21 = 0 The equation of straight line is kx-y - (4k-3) = 0 (1) It is proved that no matter why K is a real number, the line L and C must intersect (2) Let l be at the intersection of circle C, AB, what is k, and what is the minimum value of AB
Is there something wrong with your title? C in the circular equation should be y? If so, you can formulate the circular equation. You can see that the center point of the circle is a (3,4) and the radius is 2. Then you bring B (4,3) into the linear equation, and you will find that (4,3) holds no matter what the value of K is, that is, the line must pass through the point (4
The position relationship between circle O1: x2 + Y2 + 6x-7 = 0 and circle O2: x2 + Y2 + 6y-27 = 0 is______ ．
Circle O1: x2 + Y2 + 6x-7 = 0, the standard equation is (x + 3) 2 + y2 = 16, the center is (- 3, 0), the radius is 4, circle O2: x2 + Y2 + 6y-27 = 0, the standard equation is x2 + (y + 3) 2 = 36, the center is (0, - 3), the radius is 6, the center distance is 32 ∵ 6-4 ∵ 32 ∵ 6 + 4, the two circles intersect
The equation x2 + Y2 - (4m + 2) x-2my + 4m2 + 5m + 2 = 0 represents the circular equation, then the value range of real number m is
According to the problem: (x-2m-1) ^ 2 + (y-m) ^ 2 + 4m ^ 2 + 5m + 2 - (2m + 1) ^ 2-m ^ 2 = 0
(x-2m-1)^2+(y-M)^2+4m^2+5m+2-4m^2-4m-1-m^2=0
(x-2m-1)^2-(y-m)^2=m^2-m-1
To make the equation a circle, i.e. m ^ 2-m-1 > 0
(m-1/2)^2>3/4
m> (3 ^ 0.5 + 1) / 2 or M
The equation x2 + Y2 + 2ay + 2A2 + A-1 = 0 represents a circle, then the value range of real number a is?
x²+(y+a)²=-a²-a+1
Represents a circle
So - A & sup2; - A + 1 > 0
a²+a-1
RELATED INFORMATIONS
- 1. If the equation x2 + Y2 + 4mx-2y + 4m2 + 4m = 0 represents a circle, then the value range of real number m is
- 2. Find the real number m so that the straight line X-my + 3 = 0 and the circle x 2 + y 2 = 6x-5 satisfy the following conditions: (1) intersection; (2) tangency; (3) separation
- 3. If the line X-my + 3 = 0 and the circle (x-3) ^ 2 + y ^ 2 = 4 are separated, then the value range of real number m is
- 4. If the line X-my + 1 = 0 is tangent to the circle x ^ 2 + y ^ 2-2x = 0, what is the value of M
- 5. If the real number x, y satisfies X-Y + 1 > = 0, y + 1 > = 0, x + y + 1
- 6. Given that real numbers x and y satisfy 2x + y ≥ 43x + y ≤ 62x − y ≥ - 4, then the value range of Y − 2x − 2 is obtained______ ．
- 7. Given that the real number x y satisfies the constraint condition x > = 1, Y > = 0, X-Y > = 0, then the value range of Z = (Y-1) / X is? A [- 1,0] B (negative infinity, 0] C [- 1, positive infinity) d [- 1,1)
- 8. If | X-1 | + | X-2 | + | x-3 | + +|If x-2007 | is greater than or equal to a for all real numbers x, then the value range of real number a is? Well
- 9. If the real numbers x and y satisfy the constraint condition 5x + 3Y ≤ 15y ≤ x + 1x − 5Y ≤ 3, then the maximum value of Z = 3x + 5Y is______ ．
- 10. Find the function y = sin ^ 2x + acosx-5a / 8-3 / 2 (0
- 11. Given that the equation of a circle is x2 + y2-6x-8y = 0, let the longest chord and the shortest chord of the circle passing through the point (3, 5) be AC and BD respectively, then the area of the quadrilateral ABCD is () A. 106B. 206C. 306D. 406
- 12. The linear equation passing through point m (2,1) and tangent to circle x2 + y2-6x-8y + 24 = 0 is______ ．
- 13. The common tangent of circle x ^ 2 + y ^ 2 = 1 and circle x ^ 2 + y ^ 2-6x-8y + 9 = 0 are
- 14. The equation x & sup2; + Y & sup2; + ax + 2ay + 2A & sup2; + A-1 = 0 indicates the value range of garden rule a
- 15. Let circle: x ^ 2 + y ^ 2 - (2a ^ 2-4) x-4a ^ 2Y + 5A ^ 4-4 = 0, find the value range of real number a and the trajectory equation of center C
- 16. It is known that the square of the equation KX of x minus (3K-1) x + 2 (k-1) = 0. Proof: no matter what the real number k is, the equation always has real number It is known that the square of the equation KX minus (3K-1) x + 2 (k-1) = 0 Proof: no matter what the real number k is, the equation always has real roots (2) If this equation has two real roots, x1, X2, and | x1, X2 | = 2, find the value of K?
- 17. Given the function image y = KX + (3K-1) + 2, where k is a real number, it is proved that no matter what the value of K is, the image of the original function must pass through these two points RT
- 18. Given the circle C: (x-1) 2 + (y + 2) 2 = 9, the straight line L: 2ax-y + 2a-1 = 0, we prove that no matter what the real number a is, the straight line l always intersects the circle
- 19. Given the circle equation x ^ 2 + y ^ 2-2ax-4ay + 5A ^ 2-4 = 0 (a is not equal to 0), we can determine the linear equation that no matter what the value of a is cut by the circle, the chord length is 1
- 20. If a is a real number, then the linear equation of the center of the circle (x-a) 2 + (y + 2a) 2 = 1 is () A. 2x+y=0B. x+2y=0C. x-2y=0D. 2x-y=0