AP EAMCET · Maths · Circle

A circle has its centre in the first quadrant and passes through $(2, 3)$ . If this circle makes intercepts of length $3$ and $4$ respectively on $x = 2$ and $y = 3$ , its equation is

A $x^{2} + y^{2} + 3 x - 5 y + 8 = 0$
B $x^{2} + y^{2} - 4 x - 6 y + 13 = 0$
C $x^{2} + y^{2} - 6 x - 8 y + 23 = 0$
D $x^{2} + y^{2} - 8 x - 9 y + 30 = 0$

Verified Solution

Answer & Solution

Correct Answer

(D) $x^{2} + y^{2} - 8 x - 9 y + 30 = 0$

Step-by-step Solution

Detailed explanation

Consider a circle with centre be a,b. So the equation of circle will be, x2+y2-2ax-2by+c=0 ⋯1 In the question it is given that the circle passes through 2,3. Therefore, substituting x=2 and y=3 respectively in the equation 1 we get,…

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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A circle has its centre in the first quadrant and passes through 2,3. If this circle makes intercepts of length 3 and 4 respectively on x=2 and y=3, its equation is

Step-by-step Solution

A circle has its centre in the first quadrant and passes through $(2, 3)$ . If this circle makes intercepts of length $3$ and $4$ respectively on $x = 2$ and $y = 3$ , its equation is