TS EAMCET · Maths · Application of Derivatives
Let \(m\) be the slope of the normal \(L\) drawn at \((1,2)\) to the curve \(x=t^2-7 t+7, y=t^2-4 t-10\) and \(a x+b y+c=0\) be the equation of the normal L. If G.C.D of \((a, b, c)\) is 1 , then \(m(a+b+c)=\)
- A \(8\)
- B \(\frac{-64}{5}\)
- C \(-8\)
- D \(5\)
Answer & Solution
Correct Answer
(D) \(5\)
Step-by-step Solution
Detailed explanation
\(x=\mathrm{t}^2-7 t+7\) \[ \begin{aligned} & \frac{d x}{d t}=2 t-7 \\ & y=t^2-4 t-10 \\ & \frac{d y}{d t}=2 t-4 \\ & \frac{d y}{d x}=\frac{2 t-4}{2 t-7} \end{aligned} \] \(\therefore\) Slope of normal \(=\frac{7-2 t}{2 t-4}\) \(\because\) Now, at \((1,2)\) :…
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