Question

E-6.
Two circles are drawn through the point (a, 5a) and (4a, a) to touch the axis of 'y'. They
intersect at an angle of then tano is ​

Answer 1

Answer:

θ = Tan⁻¹(40/9)

Step-by-step explanation:

Equation of Circle

(x - h)² + (y - k)² = r²

(x - h)² + (y - k)² = h²   as it touches y - axis

passes through a , 5a

(a - h)² + (5a - k)² = h²

Passes through 4a , a

(4a - h)²  + (a - k)² = h²

Solving both we get

k = 3a  or 29a/3

h = 5a/2  or 205a/18

Center of  two circles

(5a/2 , 3a)  & (205a/18 , 29a/3 , )

Slope with intersection point (4a , a)

(3a - a)/(5a/2 - 4a)  = -4/3

(29a/3 - a)/(205a/18 - 4a) = 156/133

Tanθ = (-4/3 - 156/133)/(1 + (-4/3)(156/133))

=> Tanθ = (-532 - 468)/( 399 - 624)

=> Tanθ = (-1000)/( -225)

=> Tanθ = 40/9

=> θ = Tan⁻¹(40/9)