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Show that the straight line 3x +4y+6=0 touches the parabola y^2=9/2x.also find the point of contact

Show that the straight line 3x +4y+6=0 touches the parabola y^2=9/2x.also find the point of contact

Grade:12th pass

1 Answers

Arun
25763 Points
2 years ago
Dear student
 
If we compare y^2 = 9/2 x with y^2 = 4ax
then
4a = 9/2
a = 9/8
 
Now c in the line = -6/4 = -3/2
 
Now a/m = (9/8)/(-3/4) = -36/24 = -3/2
 
since c = a/ m then this line is tangent to given parabola.
 
Now point of contact = ( a/m^2 , 2a/m)

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