Solve the problem.
-Find the point on the parabola $x = t ^ { 2 } , y = t , *

Question

Solve the problem.
-Find the point on the parabola $x = t ^ { 2 } , y = t , * < t < \infty$, closest to the point $\left( \frac { 1 } { 2 } , 54 \right)$, (Hint: Minimize the square of the distance as a function of $\mathrm { t }$.)
A) $( 0,0 )$
B) $( 36,6 )$
C) $( 9,3 )$
D) $\left( \frac { 9 } { 4 } , \frac { 3 } { 2 } \right)$

Quizplus · Accepted Answer

To find the point on the parabola closest to $\left( \frac{1}{2}, 54 \right)$, minimize the square of the distance: $D(t) = (t^2 - \frac{1}{2})^2 + (t - 54)^2$. Solving $\frac{dD}{dt} = 0$ gives $t = 3$, leading to the point $(9, 3)$.

Solve the Problem x=t2,y=t,∗<t<∞x = t ^ { 2 } , y = t , * < t < \inftyx=t2,y=t,∗<t<∞

Solve the Problem $x = t ^ { 2 } , y = t , * < t < \infty$