JEE Main 1981 Mathematics question on Conic Sections
The equation 1−rx2−1+ry2=1,∣r∣<1 represents
A.
an ellipse
B.
a hyperbola
C.
a circle
D.
None of these
Show answer and solution
Correct option: B
Solution
For the equation to represent a conic of the form X²/A - Y²/B = 1, we need A and B to have the same sign (positive) for a hyperbola.
Since |r| < 1, we have -1 < r < 1, so (1-r) > 0 and (1+r) > 0. Thus both denominators are positive, meaning the equation has the form x²/(positive) - y²/(positive) = 1, which is exactly the standard form of a hyperbola.
[1981]
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