Question
Download Solution PDFThe equation 4x2 - 9y2 + 36x + 36y - 125 = 0 represents a/an
Answer (Detailed Solution Below)
Detailed Solution
Download Solution PDFCONCEPT:
The general equation of a non-degenerate conic section is: Ax2 + Bxy + Cy2 + Dx + Ey + F = 0 where A, B and C are all not zero
The above given equation represents a non-degenerate conics whose nature is given below in the table:
|
S.No |
Condition |
Nature of Conic |
|
1 |
B = 0 and A = C |
Circle |
|
2 |
B = 0 and Either A = 0 or C = 0 |
Parabola |
|
3 |
B = 0, A ≠ C and AC > 0 |
Ellipse |
|
4 |
B = 0, A ≠ C and sign of A and C are opposite |
Hyperbola |
CALCULATION:
Given: 4x2 - 9y2 + 36x + 36y - 125 = 0
By comparing the given equation with Ax2 + Bxy + Cy2 + Dx + Ey + F = 0, we get
⇒ A = 4, B = 0, C = - 9, D = 36, E = 36 and F = - 125
Here, we can see that, B = 0, A ≠ C and sign of A and C are opposite
As we know that, if B = 0, A ≠ C and sign of A and C are opposite then the non-degenerate equation represents a hyperbola
Hence, option D is the correct answer.
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