Question
The line 
x + my + n = 0 will touch the parabola y2 = 4ax, if
- m = an2
- mn = a2
- n = am2
- mn = a
m = an2
2
n = am2
Hint:
substitute the value of y in the equation of parabola and solve for x and y
The correct answer is: n = am2
ln= am2
given, lx+ my+n = 0
y = -lx/m -n/m
substituting the value of y , we get
(-lx/m -n/m)2= 4ax
Or
l2x2+2x(ln-2am2)+n2=0
since the line touches the curve, D=0
this gives us -4alm2n+ 4a2n2=0
ln= am2
a quadratic equation has equal roots if the D value is zero. this is the condition of the line touching the curve.
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-d
