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TS EAMCET · Maths · Circle

Consider the circle \(x^2+y^2-6 x+4 y=12\). The equations of a tangent of this circle that is parallel to the line \(4 x+3 y+5=0\) is

  1. A \(4 x+3 y+10=0\)
  2. B \(4 x+3 y-9=0\)
  3. C \(4 x+3 y+9=0\)
  4. D \(4 x+3 y-31=0\)
Verified Solution

Answer & Solution

Correct Answer

(D) \(4 x+3 y-31=0\)

Step-by-step Solution

Detailed explanation

We have, \[ \begin{aligned} x^2+y^2-6 x+4 y & =12 \\ \Rightarrow \quad(x-3)^2+(y+2)^2 & =25 \\ \Rightarrow \quad(x-3)^2+(y+2)^2 & =(5)^2 \end{aligned} \] Equation of tangent whose slope \(m\) is \[ y+2=m(x-3) \pm 5 \sqrt{m^2+1} \] Now, this tangent is parallel to line…