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

What is the 7th term of the arithmetic progression 3, 6, 9, 12,...?

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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 sum of all even numbers between 1 and 50?

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

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

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If a+b = 10 and ab = 21, what is the value of (a-b)^2?

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

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

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