AP EAMCET · Maths · Circle

If the length of the tangent from any point on the circle ${(x - 3)}^{2} + {(y + 2)}^{2} = 5 r^{2}$ to the circle ${(x - 3)}^{2} + {(y + 2)}^{2} = r^{2}$ is $16$ units, then the area between the two circles in sq. units is

A $32 π$
B $4 π$
C $8 π$
D $256 π$

Verified Solution

Answer & Solution

Correct Answer

(D) $256 π$

Step-by-step Solution

Detailed explanation

Let point P(x1, y1) be any point on the circle, therefore it satisfies the circle x1-32+y1+22=5r2....(i) The length of the tangent drawn from point P(x1,y1) to the circle x-32+y+22=r2 is S1 =x1-32+y1+22-r2 =5r2-r2 [from Eq. (i)] =2r Given that length of tangent is 16 units…

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 AP EAMCET

Explore more questions on app

If the length of the tangent from any point on the circle x-32+y+22=5r2 to the circle x-32+y+22=r2 is 16 units, then the area between the two circles in sq. units is

Step-by-step Solution

If the length of the tangent from any point on the circle ${(x - 3)}^{2} + {(y + 2)}^{2} = 5 r^{2}$ to the circle ${(x - 3)}^{2} + {(y + 2)}^{2} = r^{2}$ is $16$ units, then the area between the two circles in sq. units is