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

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If the ratio of two numbers is 3:5 and their HCF is 4, what are the numbers?

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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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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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If x^2 - 6x + 9 = 0, what is the value of x?

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If x^2 - 5x + 6 = 0, what are the roots?

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If x = 3 and y = 4, what is the value of x^2 + y^2?

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What is the length of the diagonal of a square with a side length of 7 cm?

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What is the sum of the first 10 positive even numbers?

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If a square has a perimeter of 64 cm, what is its area?

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