• question_answer Direction: A straight line will touch a given conic if there is only one point of intersection of the line and the given conic. If the conic is specified by quadratic equation in$x$ and $y,$ then the straight line will touch if the discriminant of the equation obtained by the elimination of one of the variable is zero. Let us consider parabola ${{y}^{2}}=8x$ and an ellipse$15{{x}^{2}}+4{{y}^{2}}=60$. The equation of the normal at the point of contact of the common tangent which makes an acute angle with the positive direction of $x-$axis to the parabola is A)  $2x+y-24=0$           B)  $2x+y-48=0$ C)  $2x+y+48=0$         D)  $2x+y+24=0$

Equation of tangent is $x-2y+8=0$              ?(i) Let the point of contact is $({{x}_{1}},\,{{y}_{1}})$ then the equation of tangent to the curve ${{y}^{2}}=8x$ is $y{{y}_{1}}-4x-4{{x}_{1}}=0$     ?(ii) On comparing Eqs. (i) and (ii), we get $\frac{1}{-4}=\frac{-2}{{{y}_{1}}}=\frac{8}{-4{{x}_{1}}}$ $\Rightarrow$            $2x+y-24=0$