Final answer:
The given equations can be classified as a circle, quadratic (parabola), hyperbola, and linear equation.
Step-by-step explanation:
The given equations are:
(x - 5)² + (y - 2)² = 16
x² + y² = 100
y² - x = 25
(x - 2)² - (y + 5)² = 10
y = 2x + 5
Let's analyze each equation to classify it:
- The equation (x - 5)² + (y - 2)² = 16 is the equation of a circle with center (5, 2) and a radius of 4.
- The equation x² + y² = 100 is also the equation of a circle with center (0, 0) and a radius of 10.
- The equation y² - x = 25 can be rearranged as x = y² - 25, which represents a quadratic (parabola) with the vertex at (-25, 0) and opening to the right.
- The equation (x - 2)² - (y + 5)² = 10 is the equation of a hyperbola with center (2, -5), horizontal transverse axis, and vertical conjugate axis.
- The equation y = 2x + 5 represents a linear equation.