Question
Download Solution PDFFind the eccentricity of conic x2 + 2x + 2y2 + 4y - 13 = 0 is .
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Standard equation of Ellipse,
Eccentricity, e =
Calculation:
x2 + 2x + 2y2 + 4y - 13 = 0
This can be written as:
x2 + 2x + 1 + 2 (y2 + 2y) - 13 - 1= 0
x2 + 2x + 1 + 2 (y2 + 2y + 1 - 1) - 13 - 1= 0
x2 + 2x + 1 + 2 (y2 + 2y + 1 - 1) - 13 - 1 - 2 = 0
x2 + 2x + 1 + 2 (y2 + 2y + 1) = 16
(x + 1)2 + 2(y + 1)2 = 16
On comparing with standard eqn. a = 4 and b = 2√2
We know that , eccentricity , e =
⇒ e =
⇒ e =
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