The straight line x+2y=1 meets the coordinate axes at A and B.

Question

The straight line $x+2y=1$ meets the coordinate axes at $A$ and $B$. A circle is drawn through $A$, $B$ and the origin. Then the sum of perpendicular distances from $A$ and $B$ on the tangent to the circle at the origin is:

Accepted Answer

Equation of circle

(x - 1) (x - 0) + (y - 0) (y - $${1 \over 2}$$) = 0

$$ \Rightarrow $$  x2 + y2 - x - $${y \over 2}$$ = 0

Equation of tangent of region is 2x + y = 0

$$\ell $$1 + $$\ell $$2 = $${2 \over {\sqrt 5 }} + {1 \over {2\sqrt 5 }}$$

= $${{4 + 1} \over {2\sqrt 5 }} = {{\sqrt 5 } \over 2}$$

Solutions · 1