Parabola Part 1

Given, parabola ⇒y2=6x
⇒‌‌y2=4(‌

3

2

)x
and given, line ⇒2x+y=1.
∵ Equation of any tangent to the parabola having slope m is
y=mx+3∕2m
Slope of line 2x+y=1 is m1=−2
∵ Tangent is perpendicular to this line,
∴ Slope of tangent =m2=−‌

1

m

=‌

1

2

∴ Equation of tangent will be
y=‌

1

2

x+‌

3

2

×2
y=‌

x

2

+3
or‌‌2y=x+6
or‌‌x−2y+6=0
Clearly, on putting the coordinates of point (5,4), the equation of tangent is not satisfied.
∴ Point (5,4) does not lie on this tangent.