EllipseHard
Question
Equation 2(x - y + 1)2 + 
(x + y + 3)2 = 36 represents an ellipse whose -
(x + y + 3)2 = 36 represents an ellipse whose -Options
A.centre is (-2,-1)
B.eccentricity is 
C.length of major axis is 6
D.equation of major axis x - y + 1 = 0
Solution
Here lines x - y + 1 = 0 and x + y + 3 = 0 are mutually perpendicular lines.
Let
= X and 
= Y
then given equation becomes,
4X2 + 9Y2 = 36 or
= 1
∴ Centre is given by solving X = 0 and Y = 0
or x - y + 1 = 0 and x + y + 3 = 0
⇒ (x, y) = (-2,-1)
Also, e =
Major axis is X = 0 i.e. x – y + 1 = 0.
Length of major axis = 2a = 2 × 3 = 6.
Let
= X and = Ythen given equation becomes,
4X2 + 9Y2 = 36 or
= 1∴ Centre is given by solving X = 0 and Y = 0
or x - y + 1 = 0 and x + y + 3 = 0
⇒ (x, y) = (-2,-1)
Also, e =
Major axis is X = 0 i.e. x – y + 1 = 0.
Length of major axis = 2a = 2 × 3 = 6.
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