| 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\[15{{x}^{2}}+4{{y}^{2}}=60\]. |
A) \[2x+y-24=0\]
B) \[2x+y-48=0\]
C) \[2x+y+48=0\]
D) \[2x+y+24=0\]
Correct Answer: A
Solution :
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 \[\frac{1}{-4}=\frac{-2}{{{y}_{1}}}=\frac{8}{-4{{x}_{1}}}\] \[\Rightarrow \] \[2x+y-24=0\]
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