Posted by dt on .
find the lines that are (a) tangent and (b) normal to the curve at the given point
x^2 + xy  y^2 = 1

12th grade calculus 
bobpursley,
Take the differential...
2xdx+ y dx + x dy 2ydy=0
solve for dy/dx
Then use that as m in
y=mx + b Puttingin the x,y point, solve for b.
then, for the normal, take the negative reciprocal of m, and again, solve for the line
y=1/m x + b 
12th grade calculus 
Reiny,
You did not state the given point.
Using implicit derivative I found it to be
y' = (2x+y)/(2yx)
sub in the given point, that gives you the slope of the tangent.
Now that you have the slope (m) and a given point, use the grade 9 method of finding the equation of the tangent.
Take the negative reciprocal of your slope, and the given point to find the equation of the normal. 
12th grade calculus 
Damon,
You forgot to say what point.
However in general we find the derivative, dy/dx and call that the slope, m, of the tangent at the point. Then plug the x and y of the point in to get b in y = m x + b
to get the derivative
2 x dx/dx +x dy/dx + y dx/dx  2 y dy/dx = 0
or
2x + y = (2yx) dy/dx
dy/dx = (2x+y)/(2yx) 
12th grade calculus 
,
thank alot

12th grade calculus 
ralonda,
4) x  4y = 31
2x  4y = 34