slope of tan line to the ellipse is -4x/y for x^(2)/4+y^(2)/16
Are there any points where the slope is not defined? (Enter them as comma-separated ordered-pairs, e.g., (1,3), (-2,5). Enter none if there are no such points.)
slope is undefined at
of course -- where y=0
To find the points where the slope is not defined for the ellipse equation x^2/4 + y^2/16, we need to find the values of x and y that make the slope expression -4x/y undefined.
The slope is undefined when the denominator, y, becomes zero since dividing by zero is undefined in mathematics.
To find the points where y is equal to zero, we can set y = 0 and solve for x:
x^2/4 + 0 = 1
x^2/4 = 1
x^2 = 4
x = ± 2
Therefore, the points where the slope is undefined are (-2, 0) and (2, 0).
So, the points where the slope is not defined for the given ellipse equation are (-2,0) and (2,0).