At what point(s) on the curve x2 + y2 = 9 is the tangent line vertical?
Answers
The points at which the tangent lines are vertical are (3.0) and (-3,0) when tangent line is vertical where(s) on the x² + y² = 9 curve.
Given that,
We have to find the tangent line is vertical where(s) on the x² + y² = 9 curve at what point.
We know that,
A vertical line has a slope that is undefined.
So, we're interested in finding out where the first derivative is undefinable.
Differentiating the equation
x² + y² = 9
2x + 2y y' = 0
y' = -2x/2y
y' = -x/y
We explore what values result in an undefined fraction for the slope of a vertical line. The fraction -x/y is undefinable when y = 0, hence y must be zero.
The effect of changing the original equation to read y = 0 is
x² + 0² = 9
x=±3
In this case there are two values of x which are 3 and -3.
Therefore, the points at which the tangent lines are vertical are (3.0) and (-3,0) when tangent line is vertical where(s) on the x² + y² = 9 curve.
To learn more about tangent visit:
https://brainly.in/question/46771883
https://brainly.in/question/38355532
#SPJ3