Question

Find the radius of the circle passing through the point $(2,6)$, two of whose diameters are $x+y=6$ and $x+2y=4$.

• A. $10$
• B. $2\sqrt{5}$
• C. $6$
• D. $4$

Answer 1

The correct option is A $10$

$x+y=6...\left(1\right)$

$x+2y=4...\left(2\right)$

Subtracting $e{q}^n$ (2) from (1), we get

$x+y=6$

$x+2y=4$

________________

$-y=2$

$y=-2$ & $x=8$

So, centre of the circle is (8,-2)

& the other point is (2,6)

Using distance formula, we get

$\sqrt{(x_2-x_1{)}^2+(y_2-y_1{)}^2}$

$\Rightarrow \sqrt{(8-2{)}^2+(-2-6{)}^2}$

$=\sqrt{(6{)}^2+(-8{)}^2}\Rightarrow \sqrt{36+64}$

$\Rightarrow \sqrt{100}=10$

$\therefore$ option (A) is correct.