Question

If $S$ is the equation of circle whose two diameters are $2x-y=3,$ $x-2y=6$ and area is $616{\text{cm}}^2,$ then which of the following is/are true?
$(\text{Take}\pi =\frac{22}{7})$

• A. Radius of the circle is $14\text{cm}$
• B. Equation of the circle is $x^2+y^2+6y-187=0$
• C. Centre of the circle is $(0,-3)$
• D. Equation of the circle is $x^2+y^2-6y-187=0$

Answer 1

Answer: (A), (B), (C)

The correct options are
A Radius of the circle is $14\text{cm}$
B Equation of the circle is $x^2+y^2+6y-187=0$
C Centre of the circle is $(0,-3)$

Solving both the diameter equation,
$2x-y=3$ and $x-2y=6$
$\Rightarrow x=0,y=-3$
Center $C(0,-3)$

Now, Area $=616{\text{cm}}^2$
$\Rightarrow \pi r^2=616\Rightarrow r^2=616\times \frac{7}{22}\Rightarrow r^2=28\times 7=196\therefore r=14$

Equation of the required circle is
$(x-0{)}^2+(y+3{)}^2={14}^2\Rightarrow x^2+y^2+6y-187=0$