X2 + Y4 = 16
find the slopes of the 2 tangent lines to the curve from (5,1)
4 answers
Are the 2 and 4 exponents?
Yes, sorry about that.
Require that
Y^4 = 16 - X^2
and also require a tangency condition that
(Y-1)/(X-5) = dY/dX
Implict differentiation results in
4Y^2 dY/dX = -2X
dY/dX = -X/(2Y^2)
Therefore
(Y-1)/(X-5) = -X/(2Y^2)
You now have two equations in two unknowns, X and Y. That should allow to solve for any (X,Y) solutions
Y^4 = 16 - X^2
and also require a tangency condition that
(Y-1)/(X-5) = dY/dX
Implict differentiation results in
4Y^2 dY/dX = -2X
dY/dX = -X/(2Y^2)
Therefore
(Y-1)/(X-5) = -X/(2Y^2)
You now have two equations in two unknowns, X and Y. That should allow to solve for any (X,Y) solutions
Thanks.
1 answer