Paragraph: Consider two circles S ₁: x ^2+ y ^2-9=0 and S ₂: x ^2+ y ^2-10 x +9=0 . Question: If is the angle between the two common tangents of S₁=0 and S₂=0 , then equals

Step-by-step solution

.x^2+y^2-10 x+9=0 circles are orthogonal x^2+y^2-9=0 (i) 1 2 (3)(4)= 1 2 51 (Area of POC written in two ways) I= 12 5 Length of common chord =2 I = 24 5 (ii) 2 = 3 a = 4 5+a 15+3 a=4 a a=15 Hence P(-15,0) Now 2 = 3 15 = 1 5 =1-2 ^2 2 =1-(2) 1 25 = 23 25 Ans. (iii) 2 = 1 5 2 = 1 24 =m_ C T = slope of their common tangent Equation of common tangent is (y-0)= 1 24 (x+15) x- 24 y+15=0 Distance from (9,0) is | 9+15 5 |= 24 5