Can some one help in finding the two lines that are tangent to the ellipse
2x2 – 4x + y2 + 1 = 0
Thank you...
There are infinitely many lines that are tangent to an ellipse, so which 2 do you want?
Also it would be much easier to understand your problem and equation if you learn latex or at least use the proper notions of symbols like ^ means to the power of...
For instance this:
or
this
2x^2 -4x + y^2 + 1 = 0
would have been easier to understand
Let be a point on the ellipse.
Thus, the derivative is
Thus,
Thus, the tangent line has the form
Since the lines pass through the origin, we see that
What do we do now?
Recall that . Thus, at the point , we get
Thus, substituting this into the mess we came up for the tangent lines, we see that
Substitution this into the expression for , we get that
Thus, at the point , the tangent line has the equation
Thus, at the point , the tangent line has the equation
Does this make sense?
--Chris
I need help with this one.
Find the tangent line(s) to the ellipse x^2 + 2y^2 +4x = 5 at the point (1,0)
I differentiated the equation implicitly to get this: (-2x-4)/4y
And thats where i got stuck. cuz i get a ZERO in the denoinator.
well,, using analytic math I got this equation (not sure if its correct either): x+5/3=0
but i HAVE TO get there using differentiation
the teacher said something like this is gonna appear on the test, so please help