Question

Angle between tangents drawn to $x^2+y^2-2x-4y+1=0$ at the points where it is cut by the line $y=2x+c,is\frac{\pi }{2}$ then

• A. $|c|=\sqrt{5}$
• B. $|c|=2\sqrt{5}$
• C. $|c|=\sqrt{10}$
• D. $|c|=2\sqrt{10}$

Answer 1

The correct option is C $|c|=\sqrt{10}$

$x^2+y^2-20-4y+1=0y=20+c$
Radius of the circle = 2
perpendicular distance of line y = 20 + c from the centre of the circle, $d=\frac{c}{\sqrt{5}}$
$cos\theta =\frac{d}{r},(\theta =\frac{\pi }{4})\frac{c}{2\sqrt{5}}=\frac{1}{\sqrt{2}}c=\sqrt{10}$