The line 2x-y+1=0 is a tangent to the circle at the point (2,5), and the centre of the cir…

Question

The line $2x-y+1=0$ is a tangent to the circle at the point $(2,5)$, and the centre of the circle lies on $x-2y=4$. Then, the radius of the circle is

Accepted Answer

$${m_1} \times {m_2} =  - 1$$

$${{{{a - 4} \over 2} - 5} \over {a - 2}} \times 2 =  - 1$$

$${{a - 14} \over {a - 2}} =  - 1$$

$a - 14 = 2 - a$

$2a = 16$

a = 8

$$ \therefore $$ Centre (8, 2)

Radius = $$\sqrt {36 + 9} $$

$$ = \sqrt {45} $$

$$ = 3\sqrt 5 $$

Solutions · 1