The chord PQ of the parabola y^2=x, where one end P of the chord is at the point (4,-2), i…

Question

The chord $PQ$ of the parabola $y^2=x$, where one end $P$ of the chord is at the point $(4,-2)$, is perpendicular to the axis of the parabola. Then the slope of the normal at $Q$ is:

Accepted Answer

$PQ\perp$ axis means $Q$ has the same $x$-coordinate as $P$: $Q=(4,2)$.

Tangent to $y^2=x$ at $(x_1,y_1)$: $yy_1=	frac12(x+x_1)$. At $(4,2)$: $2y=	frac12(x+4)\Rightarrow y=	frac{x}{4}+	frac12$, slope of tangent $=	frac14$.

Slope of normal $=-4.$

Solutions · 1