Question

If \( O A \) and \( O B \) be the tangents to the circle \( x^{2}+y^{2} \) \( -6 x-8 y+21=0 \) drawn from the origin \( O \), then \( A B= \) 

(a) 11

(b) \( \frac{4}{5} \sqrt{21} \)

(c) \( \sqrt{\frac{17}{3}} \)

(d) None of these

Answer 1

The correct option is (b) \(\frac{4}{5} \sqrt{21}\)

Equation of circle ⇒ x² + y² − 6x − 8y + 21 = 0

radius \(\Delta = \sqrt{9+16-21} = 2\)

AB is chord of contact & its equation is

x.x₁ + yy₁ + 9(x + x₁) + f(y + y₁) + c = 0

(x₁,y₁) = (0,0)

0 + 0 − 3(x + 0) − 4(y + 0) + 21 = 0

3x + 4y − 21 = 0

Perpendicular distance from (3, 4) to line l₁