Question

A triangle is formed by the lines whose combined equation is given by (x + y – 4) (xy –2x – y + 2) = 0. The equation of its circumcircle is-

• A. x² + y² –5x –3y + 8 = 0
• B. x² + y² –3x –5y + 8 = 0
• C. x² + y² –3x –5y – 8 = 0
• D. None of these

Answer 1

Answer: (B)

x² + y² –3x –5y + 8 = 0

Answer 2

The sides of triangle are x + y – 4 = 0 …(i)

x – 1 = 0 … (ii),

y – 2 = 0 … (iii)

So, the triangle is right angled at (1, 2)

The hypotenuse is x + y –4 = 0 whose ends are

(1, 3) and (2, 2)

Circumcentre is $\left( \frac { 1 + 2 } { 2 } , \frac { 3 + 2 } { 2 } \right)$ ŗ $\left( \frac { 3 } { 2 } , \frac { 5 } { 2 } \right)$ and

circum-radius is $\frac { 1 } { \sqrt { 2 } }$

\ equation of circle is $\left( x - \frac { 3 } { 2 } \right) ^ { 2 }$+ $\frac { 1 } { 2 }$

\ x² + y² –3x – 5y + 8 = 0