The equation of the line touching both the parabola y2 = 4x and x2=−32y is ax+by+c=0. Then the value of a + b +c is

The equation of tangent in terms of the slope of the parabola y2 = 4x is y=mx+1mSince (i) is also the tangent of x2 = - 32 !, wa havex2=−32mx+1mor  x2+32mx+32m=0The above equation must have equal roots.Hence, its discriminant must be zero. Therefore,(32m)2=4×1×32mi.e.,m3=18 or m=12From (i), y=x2+2  or  x−2y+4=0