TS EAMCET · Maths · Circle
If \((3,-2)\) is the centre of the circle \(\mathrm{S} \equiv x^2+y^2+2 g x+2 f y-23=0\) and A is a point on the circle \(\mathrm{S}=0\) such that its distance from a point \(\mathrm{P}(-1,-5)\) is least, then \(\mathrm{A}=\)
- A \((3,-2)\)
- B \(\left(\frac{9}{5}, \frac{28}{5}\right)\)
- C \(\left(\frac{3}{5},-\frac{2}{5}\right)\)
- D \(\left(\frac{-9}{5}, \frac{-28}{5}\right)\)
Answer & Solution
Correct Answer
(D) \(\left(\frac{-9}{5}, \frac{-28}{5}\right)\)
Step-by-step Solution
Detailed explanation
C \( = (3,-2) \) \(r = \sqrt{3^2+(-2)^2-(-23)} = \sqrt{9+4+23} = \sqrt{36} = 6\) P \( = (-1,-5) \) \(\vec{CP} = P-C = (-1-3, -5-(-2)) = (-4,-3)\) \(|\vec{CP}| = \sqrt{(-4)^2+(-3)^2} = \sqrt{16+9} = 5\)…
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