2020-수학-가형-홀수-19¶
문제¶
풀이¶
from sympy import *
c_x, c_y = symbols('c_x, c_y')
r = 4
A = Point(-r,0)
B = Point(r,0)
C = Point(c_x,c_y)
D = Rational(1,2)*(B-A)-2*(C-B)+ A
ga2 = expand((C-A).dot(C-B))
ga2
\[\displaystyle c_{x}^{2} + c_{y}^{2} - 16\]
na = expand(D.dot(D)-r**2)
na
\[\displaystyle 4 c_{x}^{2} - 32 c_{x} + 4 c_{y}^{2} + 48\]
sol = solve((ga2,na),(c_x,c_y))
sol
[(7/2, -sqrt(15)/2), (7/2, sqrt(15)/2)]
val = expand(((D-A).dot(D-A)))
val
\[\displaystyle 4 c_{x}^{2} - 48 c_{x} + 4 c_{y}^{2} + 144\]
val.subs({c_x:sol[1][0],c_y:sol[1][1]})
\[\displaystyle 40\]