## Math Problem Statement

Find the value of p, if the line 3x + 4y – p = 0 is a tangent to the circle 2 2 16 + = x y .

## Solution

## Ask a new question for Free

### By Image

Drop file here or Click Here to upload

## Math Problem Analysis

### Mathematical Concepts

Geometry

Circles

Tangents

Coordinate Geometry

### Formulas

Perpendicular distance from a point to a line: d = |Ax1 + By1 + C| / sqrt(A^2 + B^2)

Equation of a circle: x^2 + y^2 = r^2

### Theorems

Condition for a line to be tangent to a circle: The perpendicular distance from the center of the circle to the line equals the radius of the circle.

### Suitable Grade Level

Grades 9-12

## Related Recommendation

Find p for the Line Cutting a Circle in Two Points

Find the General Equation of the Circle Tangent to Line 3x - 4y = 4 at Point P(-4, -4)

Find the Tangent Line Equation for Circle A at Point Q(2, 1)

Find the Equation of a Circle Touching a Line with Radius 5

Solve the Circle Equation with Tangent Line Condition: x^2 + y^2 - 4px + (2p + 8)y + (18p - 1) = 0