JEE Mains · Maths · STD 12 - 6. Application of derivatives
If the tangent to the curve \(y=x^{3}\) at the point \(P \left( t , t ^{3}\right)\) meets the curve again at \(Q ,\) then the ordinate of the point which divides \(PQ\) internally in the ratio \(1: 2\) is
- A \(-2 t ^{3}\)
- B \(0\)
- C \(-t^{3}\)
- D \(2 t ^{3}\)
Answer & Solution
Correct Answer
(A) \(-2 t ^{3}\)
Step-by-step Solution
Detailed explanation
Slope of tangent at \(\left. P \left( t , t ^{3}\right)=\frac{ dy }{ dx }\right]_{\left( t , t ^{3}\right)}\) \(=\left(3 x^{2}\right)_{x=t}=3 t^{2}\) So equation tangent at \(P \left( t , t ^{3}\right):\) \(y-t^{3}=3 t^{2}(x-t)\) for point of intersection with \(y=x^{3}\)…
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