Math Problem Statement

Find equations of the tangents to the curve x = 9t^2 + 6, y = 6t^3 + 6 that pass through the point (15, 12).

Solution

To find the equations of the tangents to the given parametric curve that pass through the point (15,12)(15, 12), we can follow these steps:

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Math Problem Analysis

Mathematical Concepts

Parametric Equations
Tangent Lines
Calculus
Derivatives

Formulas

Parametric derivative dy/dx = (dy/dt) / (dx/dt)
Equation of a line: y - y1 = m(x - x1)

Theorems

Chain Rule

Suitable Grade Level

Grades 11-12

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