ACT (Enhanced)MathematicsMedium
A satellite is orbiting Earth. Its orbital path can be modeled by a circle centered at the origin (0,0). If the satellite passes through the point (3, 4), what is the equation of its orbital path?
- Ax^2 + y^2 = 5
- Bx^2 + y^2 = 7
- Cx^2 + y^2 = 25
- Dx^2 + y^2 = 49
Show answer & explanationAnswer & explanation
Correct answer: C. x^2 + y^2 = 25
The standard equation of a circle centered at the origin is x^2 + y^2 = r^2. Since the satellite passes through (3, 4), substitute these coordinates to find r^2, which is the radius squared.
Why the other options are wrong
- A. This is the radius (5), not the radius squared.
- B. This results from adding the coordinates instead of squaring and adding.
- D. This results from squaring the sum of the coordinates, not the individual coordinates.
Equation of a Circle (Origin)
The algebraic representation of a circle whose center is at the origin (0,0) and has a radius 'r'.
- Standard form: x^2 + y^2 = r^2.
- Any point (x, y) on the circle satisfies this equation.
- The distance formula from (0,0) to (x,y) gives the radius 'r'.
Memory trick: X squared plus Y squared, equals Radius squared, a perfect pair!