Topics › Precalculus › Hyperbola — Standard Form, Foci, and Asymptotes
Precalculus · G-GPE

Hyperbola — Standard Form, Foci, and Asymptotes

(x−h)²/a² − (y−k)²/b² = 1 (horizontal). Foci at (h±c, k) where c² = a²+b². Asymptotes y−k = ±(b/a)(x−h).

PrecalculusCommon Core HSG-GPE.A.3G-GPEVerified correct ✓

Worked examples

For the hyperbola x²/16 − y²/16 = 1, find the (positive) asymptote slope as a decimal. Asymptotes are y − k = ±(b/a)(x − h). Round to 5 decimal places.
Answer: 1
For the hyperbola (x + 2)²/16 − (y − 1)²/36 = 1, find c. Use c² = a² + b². Round to 5 decimal places.
Answer: 7.2111

Every problem on Pounce is generated and checked by code — never a wrong answer key.

Master Hyperbola — Standard Form, Foci, and Asymptotes

Code-verified problems at exactly the right level, explained the way your kid learns.

Start your free trial 🐾

Build up to this

Ellipse — Standard Form, Foci, and Key Features

More Precalculus topics

Complex Numbers in Polar Form — r(cos θ + i sin θ)Multiply and Divide Complex Numbers in Polar FormDe Moivre's Theorem — Powers and Roots of Complex NumbersVectors — Components, Addition, and Scalar MultiplicationDot Product of Vectors — Magnitude and Angle Between VectorsMatrix Addition, Subtraction, and Scalar MultiplicationMatrix Multiplication — 2×2 and 2×1 Cases2×2 Matrix Inverse and Determinant