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

Question

Accepted Answer

Correct answer: C. (c) As the straight line, y= mx+4 touches the circle x^2+4y^2=4, Put y=4x+m in x^3+4y^2=4, we get x^2+4 (4x+m )^2=4 ⇒x^2+4(16x^2+8 mx+m^2)=4 ⇒x^2+64x^2+32 mx+4(m^2-1)=0 ⇒65x^2+32 mx+4(m^2-1)=0 Since, line is tangent to the given curve ⇒D=0 ∴ (32m )^2-4 (65 ) (4(m^2-1) )=0 ⇒m= 65

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

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