Math, asked by boinem91151, 2 months ago

Find the equation of the normal to the curve y=x+1/x, x>0 perpendicular to the line 3x-4y=7

Answers

Answered by abhi178
9

Given info : The normal is normal to the curve is y = x + 1/x , x > 0 and normal perpendiculars to the line is 3x - 4y = 7.

To find : The equation of normal

solution : curve, y = x + 1/x

differentiating with respect to x,

dy/dx = 1 - 1/x²

slope of tangent of curve is dy/dx = 1 - 1/x²

a/c to question,

normal of the curve is perpendicular to the line 3x - 4y = 7 so tangent of the curve must be parallel to the line.

so, slope of tangent = slope of line

⇒1 - 1/x² = 3/4

⇒1 - 3/4 = 1/4 = 1/x²

⇒x = ±2

but x > 0 so x = 2

y = 2 + 1/2 = 5/2

now slope of normal = -1/slope of tangent = -1/(3/4) = -4/3

and now equation of normal is (y - 5/2) = -4/3(x - 2)

⇒(y - 5/2) + 4/3(x - 2) = 0

⇒3y - 15/2 + 4x - 8 = 0

⇒6y + 8x - 15 - 16 = 0

⇒8x + 6y - 31 = 0

Therefore the equation of normal is 8x + 6y - 31 = 0.

Answered by ranjanranjan6800
1

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