Topic Details (Notes format)

How to Convert Parametric Equations to Cartesian Form

Subject: Mathematics

Book: Maths Mastery

To convert parametric x=f(t), y=g(t) into Cartesian form y=F(x), eliminate the parameter t. For example, if x=2 cos(t) and y=3 sin(t), solve cos(t)=x/2, sin(t)=y/3, then sin²(t)+cos²(t)=1→ (x/2)²+(y/3)²=1. This is an ellipse in Cartesian form. Conversions matter for analyzing geometry or simplifying integrals in calculus. Recognizing how parametric forms unify with standard shapes fosters deeper insight into motion, design arcs, or advanced transformations. Mastery cements flexible modeling from parametric constraints to direct functional relationships.

Practice Questions

If a cone has a radius of 5 cm and a height of 12 cm, what is its slant height?

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The perimeter of a rectangle is 50 cm, and its length is 15 cm. What is its width?

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A sphere has a radius of 7 cm. What is its volume?

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If the perimeter of a square is 36 cm, what is the length of its diagonal?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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What is the area of an equilateral triangle with side length 10 cm?

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A car covers a distance of 150 km in 2.5 hours. What is its average speed?

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If a = 2 and b = 3, what is the value of (a^2 + b^2)?

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What is the sum of all even numbers between 1 and 100?

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The LCM of two numbers is 60, and their HCF is 5. If one of the numbers is 20, what is the other number?

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