MHT CET · Maths · Circle
A pair of tangents are drawn to the circle \(x^2+y^2+6 x-4 y-12=0\) from a point \(\mathrm{P}(-4,-5)\), then the area enclosed between these tangents and the area of the circle is
- A \(25\left(\frac{4+\pi}{4}\right)\) sq. units
- B \(25\left(\frac{4+\pi}{2}\right)\) sq. units
- C \(25\left(\frac{4-\pi}{2}\right)\) sq. units
- D \(25\left(\frac{4-\pi}{4}\right)\) sq. units
Answer & Solution
Correct Answer
(D) \(25\left(\frac{4-\pi}{4}\right)\) sq. units
Step-by-step Solution
Detailed explanation
Circle center \(C = (-3, 2)\), radius \(r = \sqrt{3^2+(-2)^2-(-12)} = 5\). Distance \(PC = \sqrt{(-4-(-3))^2+(-5-2)^2} = \sqrt{1^2+(-7)^2} = \sqrt{50}\).
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