Answer:
It has infinitely many line of symmetry. All diameters are line of symmetry.
Step-by-step explanation:
Given: Equation is x² + y² = 9
To find: line of symmetry of given equation
Given equation is the equation of circle.
x² + y² = 9
re write,
(x-0)² + (y-0)² = 3²
by comparing given equation with standard equation of circle ,
(x-h)² + (y-k)² = r²
we get, h = 0 , k = 0 , r = 3
⇒ Centre of circle = ( 0 , 0 ) and radius of circle = 3 unit
Since It is a circle. so it has Infinitely many line of symmetry
Also, All diameters of this circle are line of symmetry for this circle.
Some equation of line of symmetry,
x-axis : y = 0
y-axis : x = 0
Equation given in the question represents a circle.
Therefore, there will be infinite lines of symmetry.
Given in the question,
Equation given in the question is in the form of
[tex](x-0)^2+(y-0)^2=3^2[/tex]
Since, general equation of a circle is given by,
[tex](x-h)^2+(y-k)^2=r^2[/tex]
Therefore, given equation represents a circle.
By definition, a circle has infinite lines of symmetry passing through the center.
Therefore, given equation will have infinite lines of symmetry.
Learn more about the lines of symmetry here,
https://brainly.com/question/1968732?referrer=searchResults
