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UPCET / UPSEE Tangent through Origin — practice questions

Explore 1 free Tangent through Origin questions in UPCET / UPSEE Mathematics. Open each question or exercise to read its content, reference answers and available explanation.

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Tangent through Origin questions and exercises with answers

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If the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, then $a$ equals:Read the answer and worked solution →

Worked practice questions

If the tangent to the curve $y = e^{2x}$ at point $(a, e^{2a})$ passes through origin, then $a$ equals:

  1. 0
  2. $1/2$
  3. 1
  4. $\ln 2$
Show answer and solution

Correct answer: B. $1/2$

Slope at $(a, e^{2a})$: $y' = 2e^{2a}$. **Tangent:** $y - e^{2a} = 2e^{2a}(x - a)$. Passes through (0, 0): $-e^{2a} = 2e^{2a}(-a)$ ⇒ $1 = 2a$ ⇒ $a = 1/2$.

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