What is the equation [tex]x^2 + y^2 = 9[/tex]?

x 2 + y 2 = 9 i t ′ s a c i rc l e ce n t er : ( 0 ; 0 ) r a d i u s : r = 9 ​ = 3 l oo k a t t h e p i c t u re

Answered by Anonymous | 2024-06-10

The equation 'x squared plus y squared equals nine' represents a circle with a radius of 3, centered at the origin of a coordinate system, and is rooted in the Pythagorean theorem. The equation does not depict y as proportional to the square of x nor a parabola, but rather a circle with points (x,y) lying on its circumference.

The equation x squared plus y squared equals nine is a mathematical representation of a circle in a two-dimensional coordinate system. It is the equation of a circle with a radius of 3 centered at the origin (0,0). Any point (x, y) that satisfies this equation will lie on the circumference of this circle. Contrary to the reference stating that 'y is proportional to the square of x', which describes a parabola, this equation depicts a circle due to the presence of both x and y squared terms, which are added together. The structure of the equation reflects the Pythagorean theorem, where the sum of the squares of the two sides (x and y) of a right triangle is equal to the square of the hypotenuse (in this case, 9 is the square of the radius).
To solve for y, for example, we would rearrange the equation as follows: y squared equals nine minus x squared, and then take the square root of both sides, noting that y can be either positive or negative since the square root can produce both a positive and negative result. This yields two possible values for y for each x within the range of -3 to 3, indicating the upper and lower semicircles.

Answered by SravyaDa | 2024-06-24

The equation x 2 + y 2 = 9 describes a circle centered at the origin with a radius of 3. All points on this circle are 3 units from the origin. This equation is derived from recognizing that it follows the form of a circle's equation in the Cartesian plane.
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Answered by Anonymous | 2024-10-10