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Questions  

 If y=2x3 is a tangent to the parabola y2=4ax13 ,  then a is equal to 

a
223
b
-1
c
143
d
-143

detailed solution

Correct option is D

Solving y=2x−3 and  y2=4ax−13we have(2x−3)2=4ax−13 or  4x2+9−12x=4ax−4a3 or  4x2−4(3+a)x+9+4a3=0This equation must have equal roots, i.e., D = 0 or  16(3+a)2−169+4a3=0 or 9+a2+6a=9+4a3 or a2+14a3=0 or a=0 or a=-143

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