Question

1. the equation $4x^2 + 4y^2 = 36$ represents which conic section?

• ellipse
• circle
• hyperbola
• parabola

Explanation:

Step1: Simplify the given equation

Divide all terms by 36:
$$\frac{4x^2}{36} + \frac{4y^2}{36} = \frac{36}{36}$$

Step2: Simplify each fraction

Reduce the fractions to lowest terms:
$$\frac{x^2}{9} + \frac{y^2}{9} = 1$$

Step3: Rewrite in standard form

Combine terms to match circle form:
$$x^2 + y^2 = 9$$
This is the standard form of a circle with center at the origin and radius $3$, since the standard circle equation is $x^2 + y^2 = r^2$.

Answer:

B. circle