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Sagot :
The equation of the tangent line to the given curve (which is parallel to line (2x−y+9=0) is y−2x−3=0.
What is the equation of tangent?
There are two important elements to finding an equation that defines a tangent line: its slope and its point of contact with a curve.
The equation of the given curve is;
[tex]\rm y=x^2-2x+7[/tex]
On differentiating with respect to x, we get:
dx/dy=2x−2
The equation of the line is;
2x−y+9=0
y=2x+9
The slope of the line =2
If a tangent is parallel to line 2x−y+9=0, then the slope of the tangent is equal to the slope of the line.
Therefore, we have:
2=2x−2
2x=4
x=2
Now, at x=2
y=22−2×2+7=7
Thus, the equation of the tangent passing through (2,7) is given by,
y−7=2(x−2)
y−2x−3=0
Hence, the equation of the tangent line to the given curve (which is parallel to line (2x−y+9=0) is y−2x−3=0.
Learn more about tangent here;
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