Question

1. the equation $25x^2 + 25y^2 = 125$ represents which conic section?

options:

• parabola
• circle
• hyperbola
• ellipse

Explanation:

Step1: Normalize the equation

Divide all terms by 125:
$\frac{25x^2}{125} + \frac{25y^2}{125} = \frac{125}{125}$

Step2: Simplify the fractions

Reduce each fraction to lowest terms:
$x^2 + y^2 = 5$

Step3: Match to conic form

This fits the circle standard form $x^2 + y^2 = r^2$, where $r=\sqrt{5}$.

Answer:

circle