What is the condition that "d square + e square - 4f > 0" is the equation x square + y square + DX + ey + F representing a circle?

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• 1. Excuse me, the general equation of this circle x + y + DX + ey + F = 0, why D + e-4f > 0? How is d + e-4f > 0 obtained?
• 2. In the equation x ^ 2 + y ^ 2 + DX + ey + F = 0, if d ^ 2 = e ^ 2 = 4f, then the position of the circle () A. The length of the chord obtained by cutting two axes is equal B. Tangent to both axes C. Away from two axes D. All of the above are possible
• 3. If the center of x ^ 2 + y ^ 2 + DX + ey + F = 0 (d ^ 2 + e ^ 2-4f > 0) is on the straight line x + y = 0, then the relation of D, e, f What does F have to do with them
• 4. What are the conditions for the intersection of the circle x ＾ 2 + y ＾ 2 + DX + ey + F = 0 and the Y axis on both sides of the origin Detailed process, thank you
• 5. Calculation of Y · y ^ n 1 - 2Y ^ n * y ^ 2 y ^ n-1y ^ 3 Can you explain every step of simplification? I don't know why it's 2Y ^ n * y ^ 2 y·y^n 1 -2y^n*y^2 y^n-1y^3
• 6. The circle X & sup2; + Y & sup2; + DX + ey + F = 0 is symmetric with respect to the line y = X A.D+E=0 B.D-E=0.C.D+F=0 D.D-F=O
• 7. Let the sum of the first n terms of the sequence {an} be Sn, and 2An = Sn + 2n + 1 (n ∈ n *) (I) find A1, A2, A3; (II) prove that the sequence {an + 2} is an equal ratio sequence; (III) find the sum of the first n terms of the sequence {n · an} and TN
• 8. If a is known to be a natural number and a is not equal to 0, then () A.A is reciprocal B.A and a are reciprocal C.A and a are reciprocal each other D. A and - A are reciprocal
• 9. How much is ten and one-third minus four and one-fifth equal to forty-five and eleven eight minus (thirty and two fifths plus eight and eleven eight), etc What's ten and a third minus four and a fifth What's 45 and eight out of eleven minus (30 and two out of five plus eight and eight out of eleven) What's four and a quarter minus one and three sixteenth plus 0.75 There are three questions
• 10. The largest two odd divisors are () and the sum of all divisors is ()
• 11. The general equation of high school mathematics circle x ^ 2 + y ^ 2 + DX + ey + F = 0, f must be less than zero? What?
• 12. When d ^ 2 + e ^ 2-4f > 0, the quadratic equation x ^ 2 + y ^ 2 + DX + ey + F > 0 is called the equation of circle Is that right?
• 13. To make the two intersections of the circle x ^ 2 + y ^ 2 + DX + ey + F = 0 and the X axis on both sides of the origin,
• 14. The equation x ^ 2 + y ^ 2 + DX + ey + F = 0 is equivalent to the equation of circle A. Sufficient but not necessary condition B, necessary but not sufficient condition C, sufficient and necessary condition D, neither sufficient nor necessary condition
• 15. When the equation x + y + DX + ey + F = 0 satisfies what condition, it means circle
• 16. If the analytic expression of the function y = x ^ 2-4x + 3 is y = x ^ 2, then a =? Process
• 17. The image of the function f (x) = - 2cos (x + π / 4) is shifted a (a > 0) units to the left to get the image of the function y = g (x). If G (x) is an even function, then the image of a is a The minimum value is? Answer in detail, O (∩)_ Thank you
• 18. Given the function FX = 2sinxcosx-2cos ^ 2x + 1, the image of the function FX is shifted to the right by 6 units to get GX
• 19. After the image of the function y = 3 / x + A is shifted one unit to the left, the image C1 of y = f (x) is obtained. If the curve C1 is symmetric about the origin, then the value of real number a is
• 20. If the image of odd function y = f (x) is translated by two units along the positive direction of X axis, the resulting image is C. If C1 and C are symmetric about the origin, then C1 corresponds to the function