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

The angles of a quadrilateral are in the ratio 3:4:5:6. What is the largest angle?

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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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The perimeter of a rectangle is 40 cm, and its length is 12 cm. What is its width?

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What is the sum of the first 50 positive integers?

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What is the area of a sector of a circle with radius 14 cm and central angle 90°?

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What is the cube of 4?

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If the sum of the squares of two consecutive positive integers is 365, what are the integers?

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How many ways can 4 people sit in a row?

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If a:b = 5:7 and b:c = 6:11, what is a:c?

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