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junior college 1 | H2 Maths
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please help to determine if it's an ellipse or a circle please, thank you!
Date Posted: 4 years ago
Views: 616
Just out of curiosity, why not just punch into GC then can tell if it’s circle of ellipse? Just remember it’s ±sqrt[f(x)]
If you want to be able to tell just from looking at the equation, you’d have to familiarise yourself with the “general forms” for shapes as per mentioned by the answer provided. To add on;
Circles and ellipses have (+) sign ie x^2+y^2 or y^2+x^2. To differentiate between them, circles have same coefficients for x^2/y^2 but ellipses have different coefficients for x^2/y^2.
Hyperbolas have (-) sign ie x^2-y^2 or y^2-x^2.
When I first started JC, I was also not very used to relying on GC but eventually have to because of the sheer convenience and for future topics like differentiation/integration you can and should actually just get the answer from GC (unless otherwise states) instead of working it out manually.
If you want to be able to tell just from looking at the equation, you’d have to familiarise yourself with the “general forms” for shapes as per mentioned by the answer provided. To add on;
Circles and ellipses have (+) sign ie x^2+y^2 or y^2+x^2. To differentiate between them, circles have same coefficients for x^2/y^2 but ellipses have different coefficients for x^2/y^2.
Hyperbolas have (-) sign ie x^2-y^2 or y^2-x^2.
When I first started JC, I was also not very used to relying on GC but eventually have to because of the sheer convenience and for future topics like differentiation/integration you can and should actually just get the answer from GC (unless otherwise states) instead of working it out manually.
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For an ellipse, the idea is that the length and height must have different coefficients a and b, so that one side appears more stretched than the other.
Your question has 1x squared and 4 y squared, which means the shape is more stretched along x (see my drawing).
Hope this helps :)
Your question has 1x squared and 4 y squared, which means the shape is more stretched along x (see my drawing).
Hope this helps :)
Date Posted:
4 years ago
hi thank you for your explanation ! :) however may i clarify, if i divide 25 on the LHS as well, wont both the length of x and y be 5? meaning radius both 5, issa circle?
As there is a coefficient 4 for y squared, dividing by 25 will give you 4/25.
Whereas coefficient of x squared is 1, dividing by 25 will give you 1/25.
The length and width will still be different, so it is an ellipse.
Whereas coefficient of x squared is 1, dividing by 25 will give you 1/25.
The length and width will still be different, so it is an ellipse.
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