s^2 = 1 + 2p \Rightarrow p = \frac{s^2 - 1}{2}

Mon, 20 Apr 2026 05:50:09 +0000

# Solving $ s^2 = 1 + 2p $: How to Derive $ p = rac{s^2 - 1}{2} $ When studying quadratic equations or coordinate geometry, you may encounter relationships like $ s^2 = 1 + 2p $. This expression commonly appears in contexts involving distances and algebra — particularly when working with circles, vectors, or sloped lines. In this article, we’ll explore how to simplify $ s^2 = 1 + 2p $ into the solvable form $ p = rac{s^2 - 1}{2} $, with practical explanations and real-world applications. --- ## What Does $ s^2 = 1 + 2p $ Mean?