Topic Details (Notes format)

How to Graph a Hyperbola from Standard Form

Subject: Mathematics

Book: Maths Mastery

A hyperbola in standard form can appear as (x–h)²/a² – (y–k)²/b²=1 or (y–k)²/b² – (x–h)²/a²=1. Its center is (h,k), with transverse axis aligned to x or y. Plot the center, asymptotes, and vertices to sketch. For example, if (x–2)²/9 – (y+1)²/4=1, center is (2,–1). This conic arises in reflective properties of radio telescopes, orbits under certain conditions, or advanced geometry. Familiarity with standard forms ensures you can pinpoint orientation and asymptotes quickly, bridging conic knowledge to real-world structural or orbital designs.

Practice Questions

What is the slope of a line passing through the points (2, 3) and (4, 7)?

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The area of an equilateral triangle with side length 6 cm is:

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If x:y = 2:3 and z:y = 4:3, what is x:z?

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The LCM of 12 and 15 is:

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The probability of rolling a sum of 7 with two dice is:

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What is the sum of the interior angles of a hexagon?

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If a+b = 10 and ab = 21, what is the value of a^3 + b^3?

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If x + 1/x = 5, what is the value of x^2 + 1/x^2?

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If x + y = 10 and xy = 21, what is the value of x³ + y³?

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If x^2 + 4x + 4 = 0, what is the value of x?

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