Hello, viet,
have a look here: http://www.mathhelpforum.com/math-he...html#post26090
EB
Find the equation of the line that is tangent to the ellipse
b^2x^2 + a^2y^2 = a^2b^2 in the first quadrant and forms with the coodiante axes the triangle with smallest possible area (a and b are positive constants)
im not sure how to do this problem, the teacher explained it but it was very confusing.
Hello, viet,
have a look here: http://www.mathhelpforum.com/math-he...html#post26090
EB
Hello, viet!
Find the equation of the tangent to the ellipse [1] in quadrant 1
which forms with the coodiante axes the triangle with smallest possible area.
( and are positive constants.)
Here is a little-known (but very convenient) formula . . .
The equation of the tangent to the ellipse: . at the point
. . is given by: .
Then the intercepts of this tangent are: . and
The area of the triangle is: .
For convenience, let . Then we have: .
Differentiate: .
Equate to zero: .
Multiply by [2]
. . The ellipse is: .[1]
. . Differentiate implicitily: . [3]
Substitute [3] into [2]: . [4]
Substitute [4] into [1]: .
Substitute into [1] and get: .
Hence, the intercepts of the tangent are:
. . and
And I'll let you write the equation of that tangent line . . .