TS EAMCET · Maths · Circle
If the slope of the tangent of the circle \(S \equiv x^2+y^2-13=0\) at \((2,3)\) is \(m\), then the point \(\left(m, \frac{-1}{m}\right)\) is
- A an extemal point with respect to the circle \(S=0\)
- B an internal point with respect to the circle \(S=0\)
- C the centre of the circle \(S=0\)
- D a point on the circle \(S=0\)
Answer & Solution
Correct Answer
(B) an internal point with respect to the circle \(S=0\)
Step-by-step Solution
Detailed explanation
Given equations of circle is \[ S \equiv x^2+y^2-13=0 \] On differentiating it w.r.t \(x\), we get \[ \Rightarrow \quad \begin{aligned} 2 x+2 y \frac{d y}{d x} & =0 \\ \frac{d y}{d x} & =\frac{-x}{y} \end{aligned} \] Now, slope of tangent,…
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