Probem19+Abby,+Ben+Z.

19. Find the points on the ellipse 4x^2 + y^2 = 4 that are farthest away from point (1,0)

First, I checked to see if point (1,0) was on the ellipse: 4(1)^2 + (0)^2 = 4 4 = 4. It is.

Well in order to find the points that are farthest away, you need to use the distance formula.Also I thought it would be helpful to find domain and range. Domain is -1<x<1 and range is <-2y<2. If you set up the distance formula and plug in the endpoints both x and y? and then set the derivative=0 that should give you the right answer I think.

Ok well I found the limit as x approached 1 for the distance formula which was 0. And as x approached -1 and that was 2. Then I used substitution and got y^2=4-4x^2. I plugged this into the distance formula and got ((4-4x^2)+(x^2-2x+1))=d(x). Then I took the derivative and set it equal to 0 and after simplifying got x=-1/3. I solved for y and got 1.86. Plugging it into the distance formula, you get answer greater than 2 so the coordinates are (-.333,1.86)

