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TS EAMCET · Maths · Circle

If the line \(4 x-3 y+p=0(p+3\gt0)\) touches the circle \(x^2+y^2-4 x+6 y+4=0\) at the point \((h, k)\), then \(h-2 k=\)

  1. A \(-\frac{8}{5}\)
  2. B 2
  3. C \(\frac{6}{5}\)
  4. D 3
Verified Solution

Answer & Solution

Correct Answer

(B) 2

Step-by-step Solution

Detailed explanation

Centre \(\equiv(2,-3)\), Radius \(=3\) \(\Rightarrow\left|\frac{(4 \times 2)-(3 \times -3)+p}{5}\right|=3 \Rightarrow p+17=15 \Rightarrow p=-2\) Line is \(4 x-3 y-2=0\) \(\Rightarrow \frac{h-2}{4}=\frac{h+3}{-3}=\frac{-(8+9+p)}{25}=\frac{-3}{5}\) \(\Rightarrow h=\frac{-2}{5}\)…