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I have done question a, ,my answers are a=2, b=-2 c=141 please correct if im wrong

Please help me with with question b as i have no idea how to do it

YEEEEEET Oct 17, 2018

#1**+2 **

(a)

We can transform the original equation to this :

4x^2 + 25y^2 = 100

The center of this ellipse is at (0,0)

So..the translated equation is

4x^2 - 16x + 25y^2 + 150y = -c complete the square on x and y

4(x^2 - 4x + 4) + 25 (y^2 + 6y + 9) = -c + 16 + 225

4(x - 2)^2 + 25(y +3 )^2 = 241 - c divide through by 100

(x - 2)^2 / 25 + (y +3 ) / 4 = [241 - c ] / 100

We want the right side to = 1...so....c = 141

The center of this ellipse is at (2 , -3) so....this is the transaltion vector

So a = 2 b = -3 and c = 141

(b) The center of the translated ellipse is (2, -3)

The minor axis is parallel to the y axis

The length of this axis = 4

And the tangent lines tangent to the ellipse and parallel to the x axis are 2 units above and below the center.....so....their equations are y = -3 + 2 ⇒ y = -1 and

y = -3 - 2 ⇒ y = -5

Here's the graph : https://www.desmos.com/calculator/k2p2x4xh7k

CPhill Oct 17, 2018