The values of m for which the line y= mx+2 becomes a tangent to the hyperbola 4x^2-9y^2=36 is

Question

Accepted Answer

Correct answer: B. (b) We have, line, y= mx+2……………(i) Hyperbola, 4x^2-9y^2=36……………….(ii) On solving eqs. (i) and (ii) we get x^2(4-9m^2)-36 mx-72=0 Since, this line is a tangent of hyperbola ∴ (36m )^2+4 72(4-9m^2)=0 ⇒36 36m^2+4 36 2(4-9m^2)=0 ⇒9m^2+8-18m^2=0 ⇒9m^2=8 ⇒m^2= 89 ∴m^2= 89= 2 23

$The values of m for which the line y = mx + 2 becomes a tangent to the hyperbola 4 x^{2} - 9 y^{2} = 36 is$

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