Equation of the tangent to a perpendicular lin

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June 17th 2012, 12:56 PM
mgmanoj

Equation of the tangent to a perpendicular lin

Can someone help me to solve this : Find the equation of the tangent to the curve x² -2xy + 2y² -7x + 6y + 6 = 0 which is perpendicular to 6x + 5y -4 = 0
June 17th 2012, 01:12 PM
Plato

Re: Equation of the tangent to a perpendicular lin

Quote:

Originally Posted by mgmanoj

Can someone help me to solve this : Find the equation of the tangent to the curve x² -2xy + 2y² -7x + 6y + 6 = 0 which is perpindendicular to 6x + 5y -4 = 0

Use implicit differentiation to find $y'$ .

Find a point on the curve where $y'=\frac{5}{6}$ .
June 17th 2012, 01:30 PM
mgmanoj

Re: Equation of the tangent to a perpendicular lin

After differentiating the equation I got
dy = 2x-2y-7
dx 2x-4y-6

the slope of the tangent perpendicuar to 6x + 5y-4 = 0 is 45/6 or 5/6 - I got confused here.
June 17th 2012, 01:53 PM
Plato

Re: Equation of the tangent to a perpendicular lin

Quote:

Originally Posted by mgmanoj

After differentiating the equation I got
dy = 2x-2y-7
dx 2x-4y-6

the slope of the tangent perpendicuar to 6x + 5y-4 = 0 is 45/6 or 5/6 - I got confused here.

You know $\frac{2x-2y-7}{2x-4y-6}=\frac{5}{6}.$ Solve for either $x\text{ or }y$ and substitute into the curve.
June 17th 2012, 05:18 PM
HallsofIvy

Re: Equation of the tangent to a perpendicular lin

Quote:

Originally Posted by mgmanoj

After differentiating the equation I got
dy = 2x-2y-7
dx 2x-4y-6

the slope of the tangent perpendicuar to 6x + 5y-4 = 0 is 45/6 or 5/6 - I got confused here.

The equation 6x+ 5y- 4= 0 is the same as y= -(6/5)x+ 4/6 and has slope -6/5. The "negative reciprocal" of that is 6/5 and is the slope of the perpendicular line. I don't know where you got "45/6"! Did you mean "4/6"? Remember that the slope of the line, the number multiplying x, determines the direction, not the "constant" term.