MHT CET · Maths · Straight Lines
The circumcentre of the triangle formed by the lines \(x y+2 x+2 y+4=0\) and \(x+y+2=0\) is
- A \((0,0)\)
- B \((-2,-2)\)
- C \((-1,-1)\)
- D \((-1,-2)\)
Answer & Solution
Correct Answer
(C) \((-1,-1)\)
Step-by-step Solution
Detailed explanation
The given equation \(x y+2 x+2 y+4=0\) can be rewritten as \((x+2)(y+2)=0\) or \(x+2=0\), \(y+2=0\)
And also given that \(x+y+2=0\).
On solving the above equations, we get \(A(-2,0), B(0,-2), C(-2,-2)\)
It is clearly that \(\Delta A B C\) is right angled triangle with right angle at \(C\). Hence, centre of the circumcircle is the mid point of \(A B\) whose coordinates are \((-1,-1)\).
And also given that \(x+y+2=0\).
On solving the above equations, we get \(A(-2,0), B(0,-2), C(-2,-2)\)
It is clearly that \(\Delta A B C\) is right angled triangle with right angle at \(C\). Hence, centre of the circumcircle is the mid point of \(A B\) whose coordinates are \((-1,-1)\).
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