If the lengths of the tangents from two points A, B to a circle are 6, 7 respectively. If A, B are conjugate points then AB =
Options:
A .  
5
B .  
√85
C .  
√852
D .  
none
Answer: Option B : B Let the equation of the circle be x2 + y2=a2 and A (x1,y1), B(x2,y2) A, B are conjugate points ⇒x1x2+y1y2=a2→ (1) Length of the tangents from A, B are 6, 7 respectively ⇒√x21+y21−a2 = 6, √x22+y22−a2= 7 ⇒x21+y21−a2 = 36 x22+y22−a2 = 49 ⇒x21+y21+x21+y22−2a2 = 85 ⇒x21+y21+x21+y22−2 (x1 x2 + y1 y2) = 85 [From (1)] ⇒(x21+x22−2x1x2) + (y21+y22−2y1y2) = 85 ⇒(x1−x2)2 + (y1−y2)2 = 85 ⇒AB2 = 85 ⇒ AB = √85
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