Question

B取何值时,圆X的平方+Y的平方=4与直线Y=2X+B相切,相交,相离?

Answer 1

C:x^2+y^2= 4 (1)

L:y = 2x+b (2)

Sub (2) into (1)

x^2 + （2x+b)^2 = 4

5x^2+ 4bx + b^2-4 = 0

△ = 16b^2-20(b^2-4)

相切=>

△ = 0

16b^2-20(b^2-4) =0

-b^2+20 = 0

b^2 = 20

b = ±2√5

相交,=>

△> 0

16b^2-20(b^2-4) >0

-b^2+20 > 0

b^2 < 20

-2√5 2√5 or