Let C be a circle with radius √10 units and centre at the origin.

Question

Let $C$ be a circle with radius $\sqrt{10}$ units and centre at the origin. Let the line $x+y=2$ intersects the circle $C$ at the points $P$ and $Q$. Let $MN$ be a chord of $C$ of length 2 unit and slope $-1$. Then, a distance (in units) between the chord PQ and the chord $MN$ is

Accepted Answer

$$\text { Let the line by } x+y=\lambda$$

$$\begin{aligned}
& \therefore\left|\frac{\lambda}{\sqrt{2}}\right|=3 \
& \therefore \quad \lambda= \pm 3 \sqrt{2}
\end{aligned}$$

$$\therefore$$ distance between lines $x+y=2$ and $$x+y=3 \sqrt{2}$$ is

$$\frac{3 \sqrt{2}-2}{\sqrt{2}}=3-\sqrt{2}$$

Solutions · 1