=1 C:x2+y2=5 The equations of tangents drawn from an external point ( x1,y1 ) to hyperbola are (y−y1)=m1(x−x1) and (y−y1)=m2(x−x2) where m1,m2 are the roots of the equation (x12−a2)m2−2x1y1m ‌+y12+b2=0‌‌... ‌⇒m1m2=‌
y12+b2
x12−a2
∵m1m2=−1 (tangents are perpendicular) and (x1,y1) lies on circle ⇒‌‌x12+y12=5 From Eq. (iv), y12+b2=−x12+a2 ‌⇒‌‌x12+y12=a2−b2⇒a2−4=5 ‌⇒‌‌a2=9⇒a=3
