Explanation Given: x 2 + y 2 = ( 2 x 2 + 2 y 2 − x ) 2 Concept Used: To find an equation of the tangent line to the graph of an equation y = f ( x ) at the a point ( a , b ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) Now, the equation of the tangent line to the graph of the equation is y = m x + c Put ( a , b ) coordinate in y = m x + c to find the value of c Calculation: To find an equation of the tangent line to the curve x 2 + y 2 = ( 2 x 2 + 2 y 2 − x ) 2 at ( 0 , 1 / 2 ) First find slope of the equation at the prescribed point as: m = d y d x | ( a , b ) For that differentiate both side of the equation with respect to x as d d x ( x 2 + y 2 ) = d d x ( 2 x 2 + 2 y 2 − x ) 2 d d x x 2 + d d x y 2 = 2 ( 2 x 2 + 2 y 2 − x ) d d x ( 2 x 2 + 2 y 2 − x ) 2 x + 2 y d y d x = 2 ( 2 x 2 + 2 y 2 − x ) ( 2 d d x x 2 + 2 d d x y 2 − d d x x ) 2 x + 2 y d y d x = 2 ( 2 x 2 + 2 y 2 − x ) [ 2 ( 2 x ) + 2 ( 2 y ) d y d x − 1 ] 2 x + 2 y d y d x = 2 ( 2 x 2 + 2 y 2 − x ) [ 4 x + 4 y d y d x − 1 ] 2 x + 2 y d y d x = 8 x ( 2 x 2 + 2 y 2 − x )

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ISBN: 9781305420878

Author: Stewart

Publisher: CENGAGE L

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Chapter 3.5, Problem 79E

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To find an equation of the tangent line to the cardioid x2+y2=(2x2+2y2−x)2 at (0,1/2)

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Chapter 3.5, Problem 78E

Chapter 3.5, Problem 80E

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To find an equation of the tangent line to the cardioid x 2 + y 2 = ( 2 x 2 + 2 y 2 − x ) 2 at ( 0 , 1 / 2 )

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To find an equation of the tangent line to the cardioid x2+y2=(2x2+2y2−x)2 at (0,1/2)

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