At which points does the graph of the equation #25x^2+16y^2+200x-160y+400=0# have a vertical or horizontal tangent line?
At which points does the graph of the equation #25x^2+16y^2+200x-160y+400=0# have a vertical or horizontal tangent line?
At which points does the graph of the equation
1 Answer
Oct 17, 2016
Horizontal at (4, 0) and (4, 10) and vertical at (0, 5) and (8, 5)>
Explanation:
The equation can be reorganized to the standard form
that represents an ellipse with center C(4, 5), semi axes minor a = 4
and major b = 5 and axes parallel to the axes of coordinates..
The ends of the axes of the ellipse are A(4, 10), A'(4, 0) B(8, 5) and
B'(0, 5).
At A and A', the tangents y = 10 and y = 0 are parallel to x-axis.
At B and B', the tangents x = 8 and x = 0 are parallel to y-axis.