Topic Details (Notes format)

How to Graph an Ellipse from Standard Form

Subject: Mathematics

Book: Maths Mastery

An ellipse in standard form is (x–h)²/a² + (y–k)²/b²=1, centered at (h,k). a and b are the semi-major or semi-minor axes lengths, indicating radii along x or y directions. Plot center, move ±a horizontally, ±b vertically for reference points, and sketch a smooth oval. Ellipses model planetary orbits, lens shapes, or mechanical linkages. Understanding ellipse parameters fosters advanced geometry solutions—like finding focal points (for reflection properties) or using them in design constraints where elliptical arcs are needed.

Practice Questions

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

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If x:y = 4:5 and y:z = 2:3, what is x:z?

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What is the cube of 4?

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The ratio of two numbers is 3:5, and their sum is 64. What are the numbers?

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A triangle has angles 60°, 60°, and 60°. What type of triangle is it?

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

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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 man invests Rs. 5000 at 5% per annum simple interest. What is the total amount after 3 years?

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If a = 5 and b = 12, what is the length of the hypotenuse of a right triangle?

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