Answer:
circle
Step-by-step explanation:
The equation
x² + y² = r²
Represents a circle centred at the origin with radius r
x² + y² = 25 ← is in this form and
is a circle centre (0, 0) with r = 5
ANSWER
circle
EXPLANATION
The given equation is
[tex] {x}^{2} + {y}^{2} = 25[/tex]
To determine the type of conic, we analyze the coefficient and sign of the quadratic terms.
If the coefficient of the quadratic terms are equal and have the same sign,then the conic is a circle.
If the coefficient of the quadratic terms are equal and have opposite signs,then the conic is a hyperbola.
If the coefficient of the quadratic terms are not equal and have the same sign,then the conic is an ellipse.
Since the coefficients are all 1 and the signs are positive, the given conic is a circle.
