15) Find the equation of the tangent line to the curve y = x^2 - 2x +7 which is  (a) parallel to the line 2x - y + 9 = 0

Answers (1)

Parellel to line 2x - y + 9 = 0 means slope of tangent and slope of line is equal 
We know that the equation of line is
y = mx + c
on comparing with the given equation we get slope of line m = 2 and c = 9
Now, we know that the  slope of tangent at a given point to given curve is given by \frac{dy}{dx}
Given equation of curve is  
y = x^2 - 2x +7
\frac{dy}{dx} = 2x - 2 = 2\\ \\ x = 2
Now, when x = 2 , y = (2)^2 - 2(2) +7 =4 - 4 + 7 = 7
Hence, the coordinates are (2,7)
Now, equation of tangent paasing through (2,7) and with slope m = 2 is
y = mx + c
7 = 2 X 2 + c
c = 7 - 4 = 3
So,
y = 2 X x+ 3
y = 2x + 3
So, the equation of tangent is y - 2x = 3

 

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