Asked by julie
let x^2 + 4xy + y^2 + 3 = 0
are there any points on the curve where the tangent is horizontal or vertical? justify your answer.
are there any points on the curve where the tangent is horizontal or vertical? justify your answer.
Answers
Answered by
Damon
2 x dx + 4 x dy + 4 y dx + 2 y dy = 0
dx (2x+4y) + dy(2y+4x) = 0
dy/dx = -(2x+4y)/(4x+2y)
if the top is 0, tangent horizontal
if the bottom is zero, vertical
for example for yertical
4x=-2y
y = -2x
plug that back in the original equation
x^2 +4x(-2x) + (-2x)^2 + 3 = 0
x^2 -8x^2 +4x^2 = -3
-3 x^2 = -3
x = +/- 1
Be sure to check my arithmetic and do the other half of the problem for numerator = 0
dx (2x+4y) + dy(2y+4x) = 0
dy/dx = -(2x+4y)/(4x+2y)
if the top is 0, tangent horizontal
if the bottom is zero, vertical
for example for yertical
4x=-2y
y = -2x
plug that back in the original equation
x^2 +4x(-2x) + (-2x)^2 + 3 = 0
x^2 -8x^2 +4x^2 = -3
-3 x^2 = -3
x = +/- 1
Be sure to check my arithmetic and do the other half of the problem for numerator = 0
There are no AI answers yet. The ability to request AI answers is coming soon!