K stands for real number. The curve represented by equation kx2 + 2y2-8 = 0 is discussed

When k < 0, the curve y24-x2-8k = 1 is a hyperbola with focus on Y axis; when k = 0, the curve is two straight lines parallel to the axis, y = 2 or y = - 2; when 0 < K < 2, the curve is an ellipse with focus on X axis; when k = 2, the curve is a circle; when k > 2, the curve is an ellipse with focus on Y axis

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1. For any real number k, what is the position relationship between the line (3K + 2) x-ky-2 = 0 and the circle x ^ 2 + y ^ 2-2x-2y-2 = 0? The relationship between the center of a circle and a straight line is discussed without over fixed point method
2. For any real number k, if the line (3K + 2) x-ky-2 = 0 passes a certain point, then the fixed point
3. The line L: kx-y-4k + 3 = 0 K belongs to the positional relationship between R and x ^ 2 + y ^ 2-6x-8y + 12 = 0
4. Given the circle C: x ^ 2 + y ^ 2-8y + 12 = 0, the line L; KX + y + 2K = 0, when the value of K is, the line L is tangent to C
5. What is the position relationship between circle x ^ 2 + y ^ 2-6x + 5 = 0 and circle x ^ 2 + y ^ 2-8y + 7 = 0? What is the positional relationship between circle x ^ 2 + y ^ 2-6x + 5 = 0 and circle x ^ 2 + y ^ 2-8y + 7 = 0? Apart, intersect, circumscribe, or inscribe? How to judge their position? Now I can get the center coordinates and radius of two circles by using the conditions in the question. But what should I do next?
6. If the equation of a circle is x 2+y…… 2+kx+2y+k…… 2 = Oh, then when the area of the circle is the largest, the coordinates of the center of the circle are
7. Given the circle x2 + Y2 + KX + 2Y + K2 = 0, when the area of the circle is the maximum, the center coordinate is () A. （0，-1）B. （1，-1）C. （-1，0）D. （-1，1）
8. If the equation of a circle is x ^ 2 + y ^ 2 + KX + 2Y + K ^ 2 = 0, what is the value of K, the area of the circle is the largest? And the coordinates of the center of the circle at this time can be obtained
9. Given the equation x ^ 2 + y ^ 2 + KX + 2Y + k = 0 of a circle, if there are two tangents of the circle made by passing through the fixed point P (1, - 1), then the condition that K should satisfy is
10. Find the equation of equiaxed hyperbola passing through point a (3, - 1) and the axis of symmetry is coordinate axis______ ．
11. If the lines X + 2y-1 = 0 and y = KX are parallel to each other, then the value of the real number k is______ ．
12. Let the real numbers x and y satisfy the following conditions: ① x-y-2 ≤ 0, ② x + 2y-4 ≥ 0, ③ 2y-3 ≤ 0, then the maximum value of Y / X is Note: I hope you can give me a picture!
13. The maximum range of objective function z = 3x + 2Y is [7,9], then the range of positive real number k is
14. Given that hyperbola y = 3x and straight line y = KX + 2 intersect point a (x1, Y1) and point B (X2, Y2), and X12 + X22 = 10, find the value of K
15. If the line y = KX + 4 intersects the circle x ^ 2 + y ^ 2 = 1 or the curve y ^ 2 = x, then the value range of K is?
16. If f (x) = x ^ 3-3x ^ 2-3mx + 4 has a maximum value of 5, find the value of the real number m and the tangent equation of the curve y = f (x) passing through the origin
17. If the line y = 2x + 1 is a tangent of the curve y = x ^ 3-x-a, find the value of the real number a
18. Find a tangent of the curve y = X3 + 3x2-5, so that the tangent is perpendicular to the straight line 2x-6y + 1 = 0 - (X3 is the third power of X, 3x2 is three times the square of x)
19. RT tomorrow midterm exam this question is the original question, hope to have a concise answer Given that the curve C: y = x3-3x2 + 2x, the line L: y = KX, and the line L and the curve C are tangent to the point (x0, Y0) (x0 ≠ 0), the equation and tangent point coordinates of the line L are obtained
20. If the line y = x is the tangent of the curve y = x3-3x2 + ax, then a=______ ．