TS EAMCET · Maths · Application of Derivatives
If the normal drawn at the point P on the curve \(y^2=x^3-x+1\) makes equal intercepts on the coordinate axes, then the equation of the tangent drawn to the curve at P is
- A \(x-y=0\)
- B \(x-y=4\)
- C \(x-y=1\)
- D \(x-y=2\)
Answer & Solution
Correct Answer
(A) \(x-y=0\)
Step-by-step Solution
Detailed explanation
Given curve: \(y^2=x^3-x+1\) Differentiating w.r.t. \(x\): \(2y \frac{dy}{dx} = 3x^2-1\) Slope of tangent \(m_T = \frac{3x^2-1}{2y}\) Normal makes equal intercepts \(\implies\) slope of normal \(m_N = \pm 1\) Slope of tangent \(m_T = -\frac{1}{m_N} = \mp 1\) The options are of…
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