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Cricle in a plane

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Cricle in a plane [#permalink] New post 17 Dec 2010, 09:48
Quick question, since I haven't been able to find the answer throughout the forum. When question says that circle is Xssqrd+Ysqrd=1, does that mean that radius of a circle on an XY plane is 1?

Appreciate the help guys!
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Re: Cricle in a plane [#permalink] New post 17 Dec 2010, 09:54
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MisterEko wrote:
Quick question, since I haven't been able to find the answer throughout the forum. When question says that circle is Xssqrd+Ysqrd=1, does that mean that radius of a circle on an XY plane is 1?

Appreciate the help guys!


THEORY:
In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that:
(x-a)^2+(y-b)^2=r^2


Image

This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b.

If the circle is centered at the origin (0, 0), then the equation simplifies to:
x^2+y^2=r^2

So, if you have x^2+y^2=1 then you know that this circle is centered at the origin and has the radius equal to \sqrt{1}=1

For more check: math-coordinate-geometry-87652.html

P.S. It's better to write "Xssqrd+Ysqrd=1" as x^2+y^2=1.
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Re: Cricle in a plane [#permalink] New post 17 Dec 2010, 13:30
Bunuel wrote:
MisterEko wrote:
Quick question, since I haven't been able to find the answer throughout the forum. When question says that circle is Xssqrd+Ysqrd=1, does that mean that radius of a circle on an XY plane is 1?

Appreciate the help guys!


THEORY:
In an x-y Cartesian coordinate system, the circle with center (a, b) and radius r is the set of all points (x, y) such that:
(x-a)^2+(y-b)^2=r^2


Image

This equation of the circle follows from the Pythagorean theorem applied to any point on the circle: as shown in the diagram above, the radius is the hypotenuse of a right-angled triangle whose other sides are of length x-a and y-b.

If the circle is centered at the origin (0, 0), then the equation simplifies to:
x^2+y^2=r^2

So, if you have x^2+y^2=1 then you know that this circle is centered at the origin and has the radius equal to \sqrt{1}=1

For more check: math-coordinate-geometry-87652.html

P.S. It's better to write "Xssqrd+Ysqrd=1" as x^2+y^2=1.


Crystal clear. Helpful as always. Thank you.
_________________

[highlight]Monster collection of Verbal questions (RC, CR, and SC)[/highlight]
massive-collection-of-verbal-questions-sc-rc-and-cr-106195.html#p832142

[highlight]Massive collection of thousands of Data Sufficiency and Problem Solving questions and answers:[/highlight]
1001-ds-questions-file-106193.html#p832133

Re: Cricle in a plane   [#permalink] 17 Dec 2010, 13:30
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