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

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

View Question

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

View Question

What is the HCF of 72 and 120?

View Question

A sum of money triples itself in 12 years at simple interest. What is the rate of interest per annum?

View Question

If log(100) = 2 and log(10) = 1, what is log(1000)?

View Question

The sum of the reciprocals of two numbers is 1/4. If one number is 12, what is the other?

View Question

If the average of five consecutive odd numbers is 25, what is the largest number?

View Question

If x^3 - 3x^2 + 4 = 0, what is one root of the equation?

View Question

A train 150 m long passes a pole in 15 seconds. What is its speed?

View Question

What is the area of a sector of a circle with radius 14 cm and central angle 90°?

View Question