=1 for circle, 12−α=α−10 ⇒‌‌22=2α⇒α=11 and 12−α>0⇒α<12 α−10>0⇒α>10 ⇒ Curve represents a circle for some value of α in (10,12). Option (c) is correct. Similarly, for ellipse 12−α≠α−10 ⇒‌‌22≠2α⇒α≠11 Option (a) is wrong. for hyperbola one denominator must be positive and other negative ∴‌‌12−α>0 and α−10<0 ⇒‌‌α<12 and α<10 ⇒‌‌ Means α<10 or ‌‌12−α<0 and α−10>0 ⇒‌‌α>12 and α>10 ⇒‌‌ Means α>12 Options (b) and (d) is wrong.