The values that m can take, so that the straight line y=4 x+m touches the curve x^2+4 y^2=4 is

Step-by-step solution

As the straight line, y=m x+4 touches the circle x^2+4 y^2=4 Put y=4 x+m in x^3+4 y^2=4 , we get aligned & x^2+4(4 x+m)^2=4 & x^2+4 (16 x^2+8 m x+m^2 )=4 & x^2+64 x^2+32 m x+4 (m^2-1 )=0 & 65 x^2+32 m x+4 (m^2-1 )=0 aligned Since, line is tangent to the given curve array ll & D=0 & (32 m)^2-4(65) [4 (m^2-1 ) ]=0 & m= 65 array