The number of common tangents to the circles x²+y²=4 and x²+y²-4 x+2 y-4=0 is

Step-by-step solution

Given, circles are x²+y²=4 and x²+y²-4 x+2 y-4=0 i.e. x²+y²=4 and (x-2)²-4+(y+1)²-1-4=0 x²+y²=4 and (x-2)²+(y+1)²=9 Center and radius of circles (i) is c₁= 0,0 , r₁=2 and center and radii of circle (ii) is c₂=(2,-1), r₂=3 So, difference between c₁ and c₂= 5 Now here, gathered 1=r₂-r₁ < 5 =c₁ c₂ < 5=r₁+r₂ r₂-r₁ < c₁ c₂ < r₁+r₂ gathered Hence, there will be two common tangents.