TS EAMCET · Maths · Circle

The length (in units) of the common chord of the circles $x^{2} + y^{2} + 2 x + 3 y + 1 = 0$ and $x^{2} + y^{2} + 4 x + 3 y + 2 = 0$ is:

A $\sqrt{2}$
B $2 \sqrt{2}$
C $2$
D $4$

Verified Solution

Answer & Solution

Correct Answer

(B) $2 \sqrt{2}$

Step-by-step Solution

Detailed explanation

Common chord of two intersecting circles S1: x2+y2+2g1x+2f1y+c1=0 & S2: x2+y2+2g2x+2f2y+c2=0 is given by S1-S2=0. So, for x2+y2+2x+3y+1=0 and x2+y2+4x+3y+2=0, common chord is 2x+1=0 i.e. x=-12. Solving it with the first circle, -122+y2+3y=0 i.e.…

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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The length (in units) of the common chord of the circles x2+y2+2x+3y+1=0 and x2+y2+4x+3y+2=0 is:

Step-by-step Solution

The length (in units) of the common chord of the circles $x^{2} + y^{2} + 2 x + 3 y + 1 = 0$ and $x^{2} + y^{2} + 4 x + 3 y + 2 = 0$ is: