Question
Download Solution PDFWhat is the eccentricity of 7x2 - 9y2 = 63 ?
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFConcept:
Hyperbola:
|
Equation |
|
|
|
Equation of transverse axis |
y = 0 |
x = 0 |
|
Equation of Conjugate axis |
x = 0 |
y = 0 |
|
Length of Transverse axis |
2a |
2a |
|
Length of Conjugate axis |
2b |
2b |
|
Vertices |
(± a, 0) |
(0, ± a) |
|
Focus |
(± ae, 0) |
(0, ± ae) |
|
Directrix |
x = ± a/e |
y = ± a/e |
|
Centre |
(0, 0) |
(0, 0) |
|
Eccentricity |
|
|
|
Length of Latus rectum |
|
|
|
Focal distance of the point (x, y) |
ex ± a |
ey ± a |
Calculation:
The given equation is,
7x2 - 9y2 = 63, which can be written as,
Hence, it is a hyperbola with a2 = 9 and b2 = 7
The eccentricity will be,
e2 = 1 +
So, e2 = 1 +
Hence, e2 =
⇒ e =
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