TS EAMCET · Maths · Circle

If $(a, b)$ is the centre of the circle passing through the vertices of the triangle formed by $x + y = 6, 2 x + y = 4$ and $x + 2 y = 5,$ then $(a, b)$ is

A $(- 17, - 16)$
B $(\frac{17}{2}, \frac{19}{2})$
C $(17, 18)$
D $(\frac{- 17}{2}, \frac{- 19}{2})$

Verified Solution

Answer & Solution

Correct Answer

(B) $(\frac{17}{2}, \frac{19}{2})$

Step-by-step Solution

Detailed explanation

x+y=6......1, 2x+y=4.......2,x+2y=5......3 First apply elimination method on 1 & 2 we get, x=-2,y=8 Now take 2 & 3,we get x=1,y=2 And then take 1 & 3 we get x=7,y=-1 The vertices of triangle are the point of intersection of given…

Apply the relevant identity from the chapter and substitute the values established in the previous step, keeping the original constraint in view.

Use the simplified expression to isolate the unknown, then plug the result back into the question setup to confirm the working is internally consistent.

Cross-check against a boundary or limiting case. Both the dimensional balance and the qualitative behaviour at the extreme should agree with the candidate answer.

Combine the steps above to identify the correct option. The remaining choices each fail at least one of the consistency, dimensional, or boundary checks.

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If (a, b) is the centre of the circle passing through the vertices of the triangle formed by x+y=6, 2x+y=4 and x+2y=5, then a, b is

Step-by-step Solution

If $(a, b)$ is the centre of the circle passing through the vertices of the triangle formed by $x + y = 6, 2 x + y = 4$ and $x + 2 y = 5,$ then $(a, b)$ is