A geometry problem by A Former Brilliant Member

Geometry Level pending

Find an equation of the line tangent to the curve y = 3 x 2 − 4 x y=3x^2-4x and parallel to the line 2 x − y + 3 = 0 2x-y+3=0 .

y = 3 x − 3 y=3x-3 y = 3 x − 2 y=3x-2 y = 2 x + 3 y=2x+3 y = 2 x − 3 y=2x-3

A Former Brilliant Member by A Former Brilliant Member

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1 solution

The slope of the line is 2.

Differentiate the curve then solve for point (x,y). The point on the curve that touches the tangent line is (1,-1).

From point-slope form of an equation of a line,

y + 1 = 2(x-1)

y = 2x - 3

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