Desmume Pokemon Soulsilver Emulation

Zadanie NR6 NR7

Circle C and k are defined simple equations x2 + y2-4 * x-1 = 0 and 2 * x-y + 1 = 0.a) Prove that the line k is tangent to the circle Cb) Determine the equation of the image circle C in the symmetry line near


solution to the problem:
a) When a line is tangent to the circle is the circle has only one common point. So I must resolve the following equations to see if solutions of this system.
{x2 + y2-4 * x-1 = 0 {y = 2 * x +1
x2 + (2 * x +1) 2-4 * x-1 = 0x2 4 * x2 +4 * x +1 4 * x-1 = 05 * x2 = 0
{x = 0 {y = 1
Re. The system of equations has a solution, so simple is tangent to the circle at the point (0, 1).
b) It
calculate the center of the circle cx2 + y2-4 * x-1 = 0x2-2 * 2 * x 22 + y 2-1-22 = 0 (x-2) 2 + (y 0) 2 = 5
center circle has coordinates S (2, 0)
point of contact straight to the district calculated under a) has the coordinates P (0, 1)
Calculate Now the coordinates of the vector PS.PS = [Px-Sx, Py-Sy] = [0-2, 1 -0] PS = [-2, 1]
Now move the point S by a vector of PS and get the coordinates of the center of the circle symmetric prostej.S '= P + PS = (0,1) + [-2.1] S' = [-2, 2]
The general formula substitutes the district received coordinates of the center and radius, which is the same as the circle C.
r2 = 5S '= (-2, 2)
(x +2) 2 + (y-2) 2 = 5
x2 + y2 +4 * x-4 * y +3 = 0
Re . Balanced equation of the circle at line k has the form x2 + y2 +4 * x-4 * y +3 = 0