TS EAMCET · Maths · Circle

If a circle has its centre on the line $x - y - 1 = 0$ and passes through the points of intersection of the two circles $x^{2} + y^{2} + 2 x - 2 y - 2 = 0$ and $x^{2} + y^{2} - 2 x + 2 y - 7 = 0,$ then the centre of that circle is

A $(\frac{- 1}{2}, \frac{- 3}{2})$
B $(\frac{1}{2}, \frac{- 1}{2})$
C $(\frac{1}{3}, \frac{- 2}{3})$
D $(- 2, - 3)$

Verified Solution

Answer & Solution

Correct Answer

(B) $(\frac{1}{2}, \frac{- 1}{2})$

Step-by-step Solution

Detailed explanation

The family of circle passing through points of intersection of two circles x2+y2+2x-2y-2=0 and x2+y2-2x+2y-7=0 is given by x2+y2+2x-2y-2+λx2+y2-2x+2y-7=0 ⇒ 1+λx2+1+λy2+21-λx+2λ-1y-2-7λ=0…

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.

Same subject

Explore more questions on app

From TS EAMCET

Explore more questions on app

If a circle has its centre on the line x-y-1=0 and passes through the points of intersection of the two circles x2+y2+2x-2y-2=0 and x2+y2-2x+2y-7=0, then the centre of that circle is

Step-by-step Solution

If a circle has its centre on the line $x - y - 1 = 0$ and passes through the points of intersection of the two circles $x^{2} + y^{2} + 2 x - 2 y - 2 = 0$ and $x^{2} + y^{2} - 2 x + 2 y - 7 = 0,$ then the centre of that circle is