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
- A \(4 x+3 y+10=0\)
- B \(4 x+3 y-9=0\)
- C \(4 x+3 y+9=0\)
- D \(4 x+3 y-31=0\)
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…
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