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Calculus
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10 Jun 2020

Write the parametric equation of circle with radius as 4m and center as (-1,3) and find the slope of tangent at t = 5.

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Calculus 2
Skill
Solve problems relating to parametric curves
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Related questions


Show transcribed image text

Consider the circle as shown in the figure.

(a) Find the center and radius of the circle.

(b) Find the equation of the tangent line to the circle at the point (0,0)

(c)Β Find the equation of the tangent line to the circle at the point (6,0)

(d) Where do the tangent lines intersect?

This question builds on an earlier "rod problem": A 4-centimeterrod is attached at one end A to a point on a wheel of radius 2 cm.The other end B is free to move back and forth along a horizontalbar that goes through the center of the wheel. At timet=0 the rod is situated as in the diagram at the left below. The wheelrotates counterclockwise at 3.5 rev/sec. Thus, whent=1/21 sec, the rod is situated as in the diagram at the rightbelow.


(a) Let P be the point on the circle where the rod is attached. Write aformula for the slope of the tangent line to the circle at timet seconds:

(b) Write a formula for the slope of the rod at time t seconds: (Hint: You will need to recall the formula for thex-coordinate of the rod along the x-axis)

(c) Find the first time when the rod is tangent to the circle:______seconds.
(d) At the time in (c), what is the slope of the rod? .
(e) Find the second time when the rod is tangent to the circle:_______seconds.

(f) At the time in (e), what is the slope of the rod?

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