If the tangent at the point (1,2) on the ellipse 3 x^2+4 y^2=19 is also a tangent to the parabola y^2-k x=0 , then k=

Step-by-step solution

Equation of tangent at the point (1,2) on the ellipse 3 x^2+4 y^2=19 is 3 x 1+4 y 2=19 This is also tangent to the parabola From Eqs. (i) and (ii), we get y^2-k ( 19-8 y 3 )=0 array lrl & 3 y^2+8 k y-19 k=0 has equal roots, so & D=(8 k)^2-4(3)(-19 k)=0 & 64 k^2=-4 3 19 k & k= -57 16 . array