Explanation Given: A x + B y = 1 where A = x 0 a 2 and B = y 0 b 2 . P = ( x 0 , y 0 ) . Calculation: The standard equation of an ellipse will be given by: ( x a ) 2 + ( y b ) 2 = 1 ... ( 1 ) Now, differentiate the equation (1) with respect to x and we get: ( x a ) 2 + ( y b ) 2 = 1 2 x a 2 + 2 y b 2 d y d x = 0 d y d x = − b 2 x a 2 y [ d y d x ] ( x 0 , y 0 ) = − b 2 x 0 a 2 y 0 Therefore, the slope of the tangent line at the point P = ( x 0 , y 0 ) will be ( − b 2 x 0 a 2 y 0 ) So, the equation of the tangent to this ellipse at the point P = ( x 0 , y 0 ) will be given by: y − y 0 = − b 2 x 0 a 2 y 0 ( x − x 0

4th Edition

ISBN: 9781319050733

Author: Rogawski

Publisher: MAC HIGHER

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Vertices Of An Ellipse

In the study of the conic section of the geometry, An ellipse is a plane curve surrounding two focal points, or foci where the set of all locus of points in the plane has their sum of the distances to the two foci is constant. On the ellipse curve, it is…

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Chapter 12.5, Problem 70E

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That the equation of the tangent line at P is $A x + B y = 1$ , where $A = \frac{x_{0}}{a^{2}} and B = \frac{y_{0}}{b^{2}}$

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Chapter 12.5, Problem 69E

Chapter 12.5, Problem 71E

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CALCULUS (CLOTH)

Ch. 12.1 - Prob. 1PQ Ch. 12.1 - Prob. 2PQ Ch. 12.1 - Prob. 3PQ Ch. 12.1 - Prob. 4PQ Ch. 12.1 - Prob. 5PQ Ch. 12.1 - Prob. 6PQ Ch. 12.1 - Prob. 7PQ Ch. 12.1 - Prob. 1E Ch. 12.1 - Prob. 2E Ch. 12.1 - Prob. 3E

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That the equation of the tangent line at P is A x + B y = 1 , where A = x 0 a 2 and B = y 0 b 2

Solution Summary: The author determines that the equation of the tangent line at P is A x + B y = 1.

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That the equation of the tangent line at P is $A x + B y = 1$ , where $A = \frac{x_{0}}{a^{2}} and B = \frac{y_{0}}{b^{2}}$

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Chapter 12 Solutions

That the equation of the tangent line at P is A x + B y = 1 , where A = x 0 a 2 and B = y 0 b 2

Solution Summary: The author determines that the equation of the tangent line at P is A x + B y = 1.

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That the equation of the tangent line at P is Ax+By=1, where A=x0a2 and B=y0b2

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Chapter 12 Solutions

That the equation of the tangent line at P is $A x + B y = 1$ , where $A = \frac{x_{0}}{a^{2}} and B = \frac{y_{0}}{b^{2}}$