Topic Details (Notes format)

How to Complete the Square for Conic Sections

Subject: Mathematics

Book: Maths Mastery

To rewrite conics in standard form, group x and y terms, complete the square for each. For instance, x² + 6x + y² – 2y= 6 transforms into (x²+6x+9)+(y²–2y+1)=6+9+1 → (x+3)²+(y–1)²=16, a circle. This systematically reveals center, radius (circle), or center, axes (ellipse, hyperbola). Completing the square is essential for identifying conic type, orientation, and focal properties. Mastery ensures quick conversions from general to standard forms, enabling geometric interpretations or direct application in advanced designs and analyses.

Practice Questions

A car travels 240 km in 4 hours. What is its average speed?

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If the sum of three consecutive integers is 72, what are the integers?

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A rectangle has an area of 48 cm² and a length of 8 cm. What is its width?

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

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A cube has a side length of 4 cm. What is its volume?

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If 2x - 3 = 7, what is the value of x?

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

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If 2x = 16, what is the value of x?

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

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