AP EAMCET · Maths · Circle

If $P (- 9, - 1)$ is a point on the circle $x^{2} + y^{2} + 4 x + 8 y - 38 = 0$ , then find equation of the tangent drawn at the other end of the diameter drawn through $P$ .

A $7 x - 3 y = 60$
B $7 x - 3 y = 56$
C $7 x + 3 y = 56$
D $7 x + 3 y = 60$

Verified Solution

Answer & Solution

Correct Answer

(B) $7 x - 3 y = 56$

Step-by-step Solution

Detailed explanation

We have a circle, x2+y2+4x+8y-38=0 ⇒x+22+y+42=58 with centre-2, -4 and radius 58 Now, there is a point P-9, -1 on the given circle. Let there is a point Qx1, y1 on the other end of the diameter drawn through point P. Hence,…

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 P(-9,-1) is a point on the circle x2+y2+4x+8y-38=0, then find equation of the tangent drawn at the other end of the diameter drawn through P.

Step-by-step Solution

If $P (- 9, - 1)$ is a point on the circle $x^{2} + y^{2} + 4 x + 8 y - 38 = 0$ , then find equation of the tangent drawn at the other end of the diameter drawn through $P$ .