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

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

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If sin(θ) = 0.6 and θ is acute, what is cos(θ)?

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A sum triples in 20 years at simple interest. What is the rate of interest per annum?

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A number is increased by 20% and then decreased by 10%. What is the net change?

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What is the value of log₃(27)?

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If a:b = 7:9 and b:c = 5:6, what is a:c?

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A square is inscribed in a circle with a radius of 5 cm. What is the area of the square?

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What is the square root of 144?

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

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

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