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
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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
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