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Find the Equation of the Tangent Line to the Curve Y = X2 − 2x + 7 Which is - Mathematics

Find the equation of the tangent line to the curve y = x2 − 2x + 7 which is

(a) parallel to the line 2x − y + 9 = 0

(b) perpendicular to the line 5y − 15x = 13.

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Solution

`The equation of the given curve is y = x2 − 2x + 7 

On differentiating with respect to x, we get:

`dy/dx = 2x - 2`

(a) The equation of the line is 2x − y + 9 = 0.

2x − y + 9 = 0 ⇒ y = 2+ 9

This is of the form y = mx c.

∴Slope of the line = 2

If a tangent is parallel to the 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

(b) The equation of the line is 5y − 15x = 13.

5y − 15x = 13 ⇒ `y = 3x + 13/5`

This is of the form y = mx c.

∴Slope of the line = 3

If a tangent is perpendicular to the line 5y − 15x = 13, then the slope of the tangent is

 

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APPEARS IN

NCERT Class 12 Maths
Chapter 6 Application of Derivatives
Q 15 | Page 212
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