Find vertical tangent
Find the point(s) on the curve at which the tangent line is(are) vertical given the curve x2+xy+y2=3
Now, vertical tangents occur where the slope is undefined. When the denominator is 0.
Set the denominator equal to 0 and solve for y. Sub this back into the original and solve for the x. y coordinates follow.
So I set the denominator equal to 0.
so I plug these two back into the original equation x2+xy+y2=3 to find the x and y points for the tangent points right?
Those are not two separate equations. Putting y= -x/2 into [tex]x^2+ xy+ y^2= 3[/tex] gives [tex]x^2- x^2/2+ x^2/4=3x^2/4= 3[/tex]. Solve that for x and then use y= -x/2 to find the corresponding values for y. OR put x= -2y into the equation: [tex]4y^2- 2y^2+ y^2= 3y^2= 3[/tex]. Solve that for y and then use x= -2y to find the correspondinmg values for x.