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

What is the cube root of 729?

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A number is increased by 20% and then decreased by 20%. What is the net change?

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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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If the length of a rectangle is doubled and the width is halved, what is the change in area?

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

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What is the sum of all angles in a hexagon?

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If a right triangle has legs of 9 cm and 12 cm, what is the length of the hypotenuse?

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What is the probability of drawing a king from a standard deck of 52 playing cards?

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

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If sin(A) = 1/2 and A is acute, what is the value of A?

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