Explanation Given information : The equation of the circle is x 2 + y 2 = r 2 . Concept used : The slope of tangent line at a point P is equal to the perpendicular slope of line C P .where C is the centre of the circle. Proof : Given equation of the circle is x 2 + y 2 = r 2 . Slope of C P is y 0 x 0 , where C is centre = ( 0 , 0 ) and P is point on the circle. The slope of tangent line is m = − x 0 y 0 Thus, the equation of the tangent line at the point P ( x 0 , y 0 ) with slope m is y − y 0 = m ( x − x 0 ) ⇒ y − y 0 = ( − x 0 y

7th Edition

ISBN: 9781524916817

Author: SMITH KARL J, STRAUSS MONTY J, TODA MAGDALENA DANIELE

Publisher: Kendall Hunt Publishing

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Chapter 2, Problem 83SP

To determine

Toshow : That the tangent line to the circle x2+y2=r2 at the point (x0, y0) has the equation y0y+xox=r2 .

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Chapter 2, Problem 82SP

Chapter 2, Problem 84SP

Chapter 2 Solutions

Calculus

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Toshow : That the tangent line to the circle x 2 + y 2 = r 2 at the point ( x 0 , y 0 ) has the equation y 0 y + x o x = r 2 .

Solution Summary: The author explains that the tangent line at the point (x_0,

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Toshow : That the tangent line to the circle x2+y2=r2 at the point (x0, y0) has the equation y0y+xox=r2 .

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Chapter 2 Solutions