First slide

Ellipse

Question

$\frac{x^{2}}{r^{2} - r - 6} + \frac{y^{2}}{r^{2} - 6 r + 5} = 1$ will represent an ellipse if r lies in the interval

Moderate

A

$(- \infty, - 2)$
B

$(3, - \infty)$
C

$(5, - \infty)$
D

$(1, \infty)$

Solution

$r^{2} - r - 6 > 0 and r^{2} - 6 r + 5 > 0 or (r - 3) (r + 2) > 0 and (r - 1) (r - 5) > 0 or (r < - 2 or r > 3) and (r < 1 or r > 5) i.e., r < - 2 or r > 5 Also, r^{2} - r - 6 \neq r^{2} - 6 r + 5 or r \neq \frac{11}{5}$

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