Question

As the point $N$ moves along the line $y=a$ in the accompanying figure, $P$ moves in such a way that $O P=M N .$ Find parametric equations for the coordinates of $P$ as functions of the angle $t$ that the line $O N$ makes with the positive $y$ -axis. (FIGURE CAN'T COPY)

          As the point $N$ moves along the line $y=a$ in the accompanying figure, $P$ moves in such a way that $O P=M N .$ Find parametric equations for the coordinates of $P$ as functions of the angle $t$ that the line $O N$ makes with the positive $y$ -axis.
(FIGURE CAN'T COPY)

Added by Kathleen S.

Calculus: Early Transcendentals

James Stewart 8th Edition

Instant Answer

Solved by Expert Carson Merrill

03/21/2023

Step 1

Since $M$ is the midpoint of $OP$, we have $M = \left(\frac{x_O+x_P}{2}, \frac{y_O+y_P}{2}\right)$. Since $O$ is the origin, we have $x_O = y_O = 0$. Also, since $P$ moves in such a way that $OP=MN$, we have $MN = OP = \sqrt{x_P^2+y_P^2}$. Therefore, $N$ has Show more…

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As the point $N$ moves along the line $y=a$ in the accompanying figure, $P$ moves in such a way that $O P=M N .$ Find parametric equations for the coordinates of $P$ as functions of the angle $t$ that the line $O N$ makes with the positive $y$ -axis.