A tangent is drawn to the parabola y^2=6x, which is perpendicular to the line 2x+y=1.

Question

A tangent is drawn to the parabola $y^2=6x$, which is perpendicular to the line $2x+y=1$. Which of the following points does not lie on it?

Accepted Answer

Perpendicular to slope $-2$ means slope $\frac12$. For $y^2=6x$ ($4A=6,A=\frac32$): tangent $y=mx+\dfrac Am=\dfrac12x+3$, i.e. $x-2y+6=0$.

Checking: $A,B,D$ satisfy this equation; $(5,4)$: $5-8+6=3
e0$ --- does not lie on it.

Solutions · 1