Power of Point Calculator
Verified Calculation Engine
The online Power of Point Calculator helps you calculate instantly and solve problems related to Coordinate Geometry Conics. This tool provides accurate results using standard formulas and step-by-step calculation; you can view the formula with example in the calculator where available. Whether you are a student, teacher, or professional, this calculator simplifies complex calculations and saves time. Enter the required values below and get instant results. Results are shown clearly, with optional step-by-step explanation where applicable. The tool is free to use and works in any modern browser—no download or installation required. Bookmark this page for quick access whenever you need reliable Math Numbers calculations.
Calculates power of a point with respect to a circle: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c. If P > 0, point is outside; P = 0, on circle; P < 0, inside.
Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0:
P = x₁² + y₁² + 2gx₁ + 2fy₁ + c
If P > 0: point outside circle
If P = 0: point on circle
If P < 0: point inside circle
Length of tangent from external point = √P
Power of point determines position relative to circle
Inputs
Results
Worked Examples
Example 1: Basic
Find power of point (5, 0) with respect to circle x² + y² = 9
- circle: x^2 + y^2 = 9
- point: (5, 0)
- power: 16
- position: Outside circle
- tangentLength: 4
Example 2: Board Level
Find power of point (1, 2) with respect to circle x² + y² - 4x - 6y + 9 = 0
- circle: x^2 + y^2 - 4x - 6y + 9 = 0
- point: (1, 2)
- power: -1
- position: Inside circle
- tangentLength:
About this calculator
Overview
Power of Point Calculator evaluates Power of Point for the math / coordinate-geometry-conics library. Primary input cue: Circle Equation [required]: Circle equation x² + y² + 2gx + 2fy + c = 0. Method anchor: Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c If P > 0: point outside circle If P = 0: point on ci.
When to use
Appropriate when power of point is the target quantity and the form fields match your known data.
Inputs explained
- Circle Equation [required]: Circle equation x² + y² + 2gx + 2fy + c = 0
- Point (x₁, y₁) [required]: Point coordinates
Formula / method
Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c If P > 0: point outside circle If P = 0: point on circle If P < 0: point inside circle Length of tangent from external point = √P. Power of point determines position relative to circle (calculator id: power-of-point-calculator).
Worked example
Worked values: circle = x^2 + y^2 = 9, point = (5, 0) → power = 16, position = Outside circle, tangentLength = 4
Interpreting results
Cross-check with a simple numeric example before relying on extreme inputs for power of point.
Assumptions
- Units (when shown) must be consistent across inputs for power of point. [power-of-point-calculator]
- Empty required inputs are not silently replaced with zeros for power of point.
- Real-number arithmetic is used unless power of point explicitly needs integers.
Limitations
- This page does not provide a full textbook proof for every identity related to power of point.
- Power of Point Calculator cannot invent missing inputs; incomplete forms stop short of a forged power of point value.
- Complex/branch cuts and undefined points are not always interactively annotated for power of point.
Important note
Educational mathematics tool. Check edge cases and domain restrictions when results look unexpected.
How to Use This Calculator
- Enter the required values in the input fields.
- Click the Calculate button.
- View the computed result instantly.
Formula Used
Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c If P > 0: point outside circle If P = 0: point on circle If P < 0: point inside circle Length of tangent from external point = √P. Power of point determines position relative to circle (calculator id: power-of-point-calculator).
Example Calculation
Worked values: circle = x^2 + y^2 = 9, point = (5, 0) → power = 16, position = Outside circle, tangentLength = 4
Frequently Asked Questions
What is Power of Point Calculator?
- Power of Point Calculator evaluates Power of Point for the math / coordinate-geometry-conics library. Primary input cue: Circle Equation [required]: Circle equation x² + y² + 2gx + 2fy + c = 0. Method anchor: Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c If P > 0: point outside circle If P = 0: point on ci.
How does Power of Point Calculator work?
- Power of point (x₁, y₁) with respect to circle x² + y² + 2gx + 2fy + c = 0: P = x₁² + y₁² + 2gx₁ + 2fy₁ + c If P > 0: point outside circle If P = 0: point on circle If P < 0: point inside circle Length of tangent from external point = √P. Power of point determines position relative to circle (calculator id: power-of-point-calculator).
Why use this Math Numbers calculator?
- Appropriate when power of point is the target quantity and the form fields match your known data.