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Unformatted text preview: Lucas Vascocu February 14, 2008 Math 241 Extra Credit Let (a,b) be such a point on the ellipse. It satisfies the equation of the ellipse: a 2 + 4b 2 = 36. Now to obtain the derivative of the ellipse: x 2 + 4y 2 = 36 >>> 2x + 8y(dy/dx) = 0 >>> 8y(dy/dx) = 2x >>> dy/dx = (2x/8y) >>> dy/dx = x/4y At such a point (a,b) the slope of the tangent line is –a/4b. Thus using the slope form of the line: (yb) = (a/4b)(xa) Multiply by 4b to simplify the equation: 4by  4b 2 = ax + a 2 >>> 4by + ax = a 2 + 4b 2 >>> 4by + 4ax = 36 4by + ax = 36 is now the tangent line of the ellipse at the point (a,b). Now, the tangent line must contain the point (12,3). Thus, 12a + 12b = 36 while a + b = 3. Obtaining this information, we get two values for b....
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This note was uploaded on 04/08/2008 for the course MATH 241 taught by Professor Camp during the Spring '08 term at LA Tech.
 Spring '08
 camp
 Math, Derivative

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