Question

If the angle between the tangent t The circle x² + 4² + 2x + 4y – 11 = 0 from p(3, 3) is  `tan^-1(a/b)` where a and b are relatively prime then the value of a – 3b is ______.

Options

• 15

• 0

• 13

• 8

Answer 1

If the angle between the tangent t The circle x² + 4² + 2x + 4y – 11 = 0 from p(3, 3) is  `tan^-1(a/b)` where a and b are relatively prime then the value of a – 3b is 13.

Explanation:

Centre C(–1, –2) radius = 4

QP = 5 tanθ = `4/5`

2Q = `tan^-1((2.4.5)/(25 - 16))` = `tan^-1(40/9)`

a = 40, b = 9

⇒ a – 3b = 13