Question

Solve y2-2pxy+p2 (x2-1)=m2

Answer 1

y² - 2Pxy + P² (x² - 1) = m²
⇒ y² - 2Pxy + P²x² - P² = m²
⇒ y² - 2Pxy + (Px)² = P² + m²
⇒ (y - Px)² = {√(P² + m²)}²
taking square root both sides,
y - Px = ± √(P² + m²)
⇒ y = Px ± √(P² + m²)

Hence, given equation is combination of two straight line equations
e.g., y = Px + √(P² + m²) and y = Px - √(P² + m²)