Question

The lines y - y1 = m (x - x1) +- a root(1 + m²) are tangents to the same circle. The radius of the circle is : (A) a/2 (B) a (C) 2a (D) none ​

Answer 1

The lines y - y1 = m (x - x1) +- a root(1 + m²) are tangents to the same circle. The radius of the circle is A a/2

Answer 2

Answer:

Option B : a

Step-by-step explanation:

The tangent on circle will have a distance of r (radius) from the centre.

Let the equation of tangent be: L1:  $(y - y1) = m(x-x1) + c$  where (x1,y1) is centre of circle.
The distance of point (x1,y1) from L1  = $|((y1-y1) -(x1-x1) -c)/\sqrt{1+m^{2} } |$

                                                                $r =$    $| c / \sqrt{1+m^{2} } |$  

                                                               c   =   ±r $\sqrt{1+m^{2} }$

Parametric equation of tangents on circle of radius r with slope m is given by (y - y1) = m (x - x1) ± r√(1 + m²) where (x1,y1) is centre of the circle.

In the given question , c = ± a$\sqrt{1+m^{2} }$

Therefore , r = a

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