Question

The lines $2x-3y=5$ and $3x-4y=7$ are two diameters of a circel of area $154sq.$ units. Then the equation of circle is

• A. $(x+1{)}^2+(y+1{)}^2=49$
• B. $(x-1{)}^2+(y-1{)}^2=-49$
• C. $(x-1{)}^2+(y+1{)}^2=49$
• D. $(x+1{)}^2+(y-1{)}^2=49$

Answer 1

The correct option is C $(x-1{)}^2+(y+1{)}^2=49$

Circle area $=\pi r^2=154\Rightarrow r=7sq.units$

intersection of diameter

$(2x-3y=5)\times 3(3x-4y=7)\times 2\_\_\_\_\_\_\_\_\_\_\_\_-y=1\Rightarrow y=-1$

$2x=5-3=2\Rightarrow x=1$

eqn of circle $\Rightarrow (x-1{)}^2+(y+1{)}^2=49$