Explanation Given information : we have given an equation of parabola and a point ( 1 , 3 ) . Let m be the slope of the tangent then the equation of tangent is y − 3 = m ( x − 1 ) ⇒ y = 3 + m ( x − 1 ) We substitute the value of y in the equation of parabola then we get ⇒ 3 x 2 = 3 + m ( x − 1 ) ⇒ 3 x 2 − m x + ( m − 3 ) = 0 For the tangent line the roots of the equation must be equal. So the discriminant of the quadratic equation must be 0

Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

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Chapter 8.2, Problem 77E

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To compute : Find the equation of tangent line at (1,3) on the parabola y=3x2

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Chapter 8.2, Problem 76E

Chapter 8.2, Problem 78E

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Chapter 8 Solutions

Precalculus: A Unit Circle Approach, Books a la Carte Edition plus MyMathLab with Pearson eText -- Access Card Package (2nd Edition)

Ch. 8.2 - Prob. 1E Ch. 8.2 - Prob. 2E Ch. 8.2 - Prob. 3E Ch. 8.2 - Prob. 4E Ch. 8.2 - Prob. 5E Ch. 8.2 - Prob. 6E Ch. 8.2 - Prob. 7E Ch. 8.2 - Prob. 8E Ch. 8.2 - Prob. 9E Ch. 8.2 - Prob. 10E

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Find the equation of tangent line at ( 1 , 3 ) on the parabola y = 3 x 2

Solution Summary: The author explains that the equation of tangent line is y-3=6(x-1).

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To compute : Find the equation of tangent line at (1,3) on the parabola y=3x2

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Chapter 8 Solutions