Rewrite the equation in a rotated xysystem without an xyterm

Rewrite the equation in a rotated x\'y\'-system without an x\'y\'-term. Express the equation involving x\' and y\' in the standard form of a conic section. Use the rotated system to graph the equation. 26x^2 - 24xy + 33y^2 - 34 = 0 (a) Choose the equivalent equation in a rotated x\'y\'-system without an x\'y\'-term. 42x\'^2 - 17y\'^2 = 34 17x\'^2 - 42y\'^2 = 34 42x\'^2 + 17y\'^2 = 34 y 17x\'^2 + 42y\'^2 = 34 (b) Express the equation involving x\' and y\' in the standard form of a conic section.

Solution

a) You have the answer for first : 17x\'^2 + 42y\'^2 = 34

b) from part a) 17x\'^2 + 42y\'^2 = 34

divide both sides by 34:

17x\'^2/34 + 42y\'^2/34 = 34/34

x\'^2/2 + 3y\'^2/2 =1

x\'^2/2 + y\'^2/(17/21) =1