ensider a circle with center at the origin and with radius 3. a. What is the equation of the circle in standard form? b. Express the distance of the point (4, 7) from any point on the circle as a function of a single variable. Note that the distance D between points (x,, y,) and (x,, y,) in a two-dimensional Cartesian plane is given as D=, C. Using the concept of derivatives and optimization, determine the point on the circle closest to (4, 7).

ensider a circle with center at the origin and with radius 3. a. What is the equation of the circle in standard form? b. Express the distance of the point (4, 7) from any point on the circle as a function of a single variable. Note that the distance D between points (x,, y,) and (x,, y,) in a two-dimensional Cartesian plane is given as D=, C. Using the concept of derivatives and optimization, determine the point on the circle closest to (4, 7).

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter10: Analytic Geometry

Section10.4: Analytic Proofs

Problem 32E

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Suppose that the circle with center 0, 0 and radius length r contains the point a,b. Find the slope of the tangent line to the circle at the point a,b.

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