COMEDK · Maths · 27. Application of Derivatives
The tangent and the normal drawn to the curve \(y=x^{2}-x+4\) at \(P(1,4)\) cut the \(X\)-axis at \(A\) and \(B\) respectively. If the length of the subtangent drawn to the curve at \(P\) is equal to the length of the subnormal, then the area of the \(\triangle P A B\) in square units is,
- A 16
- B 8
- C 32
- D 4
Answer & Solution
Correct Answer
(A) 16
Step-by-step Solution
Detailed explanation
Given, equation of curve is \(y=x^{2}-x+4\) Slope of tangent at \(P(1,4)\) is \(\frac{d y}{d x}=2 x-1 \Rightarrow\left(\frac{d y}{d x}\right)_{(1,4)}=2-1=1\) So, equation of tangent is \(y-4=1(x-1)\) \(\Rightarrow \quad y-x=3...(i)\) and cquation of normal at point \(P(1,4)\) is…
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