Math Extra Credit

Math Extra Credit - Lucas Vascocu February 14, 2008 Math...

Info iconThis preview shows pages 1–2. Sign up to view the full content.

View Full Document Right Arrow Icon

Info iconThis preview has intentionally blurred sections. Sign up to view the full version.

View Full DocumentRight Arrow Icon
This is the end of the preview. Sign up to access the rest of the document.

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: (y-b) = (-a/4b)(x-a) 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....
View Full Document

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.

Page1 / 3

Math Extra Credit - Lucas Vascocu February 14, 2008 Math...

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online