Hyperbola - practice problems
A hyperbola is a conic section consisting of two separate curves (branches) that mirror each other, defined as the set of points where the difference of distances to two foci is constant. The standard equation is (x²/a²) - (y²/b²) = 1 for horizontal hyperbolas or (y²/a²) - (x²/b²) = 1 for vertical ones. Hyperbolas have two asymptotes that the branches approach but never touch. Key features include vertices, foci, center, and the transverse and conjugate axes. Applications include navigation systems (LORAN), physics (approach trajectories), and cooling tower designs. Students learn to identify hyperbola components, sketch graphs, and distinguish them from other conic sections.Task: Work through each problem with care and demonstrate your solution process for each one.
Number of problems found: 4
- Equation - inverse
Solve for x: 7: x = 14:1000 - Hyperbola equation Find the hyperbola equation with the center of S [0; 0], passing through the points: A [5; 3] B [8; -10]
- Hyperbola
Find the equation of hyperbola that passes through the point M [30; 24] and has focal points at F1 [0; 4 sqrt 6], F2 [0; -4 sqrt 6]. - The tangent of the hyperbola
Write the equation of the tangent of the hyperbola 9x²−4y²=36 at the point T =[t1,4].
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