# Find parameter p so that y - 3x is a tangent line to y - x^2 - p

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### 1 Answer

You need to write the equation of the curve and the equation of the line such that: `y - x^2 - p = 0 and y - 3x = 0` .

Write the equation of the tangent line in the slope intercept form:

`y = 3x`

The slope of this line is m = 3 and it represents the derivative of the curve.

Differentiating the equation of the curve yields: `dy/dx = 2x` .

Since `dy/dx = m = 3 =gt 3 = 2x =gt x = 3/2` (the x coordinate of the tangency point)

Replacing x by `3/2` in the equation of the line yields:

`y = 3*3/2 = 9/2` (the y coordinate of the tangency point)

Replacing `x = 3/2` and y by `9/2` in the equation of the curve yields:

`9/2-9/4 - p = 0`

Adding p both sides yields: `p = 9/2-9/4 =gt p = 9/4`

**Evaluating the parameter p yields: `p = 9/4` .**