UPSEE Solved Model Paper 4

Consider equation

x2

a2

+

y2

b2

= 1 to represent an ellipse equation
a > 0 , b > 0 , a ≠ b
Given equation

x2

(8−t)

+

y2

(t−4)

= 1
⇒ (8 - t) > 0 and
(t - 4) > 0 , (8 - t) ≠ (t - 4)
⇒ t ∊ (- ∞ , 8) ∩ (4 , ∞) ∩ {t ≠ 6}
⇒ t ∊ (4 , 8) - {6}