## Writing Your Outline For Class 1

Let's make parallel translation of the beginning of coordinates in a point. Thus coordinates x, y of any point of M of the plane in system of coordinates of xOy and coordinate x’, y’ in new system of coordinates of x'O'y' are connected by ratios:

Let's write the equations of axes of initial system of coordinates. From a task 2 it is known that a point About’ (2, – the center of this curve. From there O’X axis slope is known. Let's write the equations of axes of new system of coordinates of XO'Y in initial system of coordinates of xOy. As the XO'Y system – initial for this hyperbole, its center is in the center of a curve – a point About’ (2, t. axes of O'X and O'Y pass through a point About’. The equation of the straight line passing through this point with the set slope of k has an appearance:

Let's make parallel translation of the beginning of coordinates in a point. Thus coordinates x, y, z of any point of M of the plane in system of coordinates of Oxyz and coordinate x’, y’, z’ in new system of coordinates of O'x'y'z' are connected by ratios:

If I2> 0, the equation (defines a curve of elliptic type. Therefore, if, this curve is a curve of elliptic type. But at this I1I3 = (1-)(4885-30 <0, and according to signs of curves of the second order (I2> 0, I1I3

where h – any real number. The equations (are 1 the equations of circles with a radius decreasing with increase in h, with the centers by O’Z axes in points of C (0, 0, h). The XO'Y plane (h = crosses an ellipsoid on a circle:

i.e. sections in such values h will represent points in the center of coordinates of the received sections. At we receive a negative number under a root, i.e. at such values h the XO'Y plane does not cross this ellipsoid. At we receive a circle: