Asked by Mike
Find an equation of the tangent line to the parabola at the given point, and find the x-intercept of the line.
17) x^2=2y , (-3,9/2)
18) y=-2x^2 , (-1,-2)
17) x^2=2y , (-3,9/2)
18) y=-2x^2 , (-1,-2)
Answers
Answered by
drwls
I'll do one of them. Use the same method for the other.
17) y = x^2/2 and the slope of the parabola is dy/dx = x
When x = -3, y = 9/2 and the slope is -3. A straight line going through (-3, 9/2) with slope -3 has the equation
y - 9/2 = -3[x -(-3)]
y = -3x + 9/2 -9 = -3x -9/2
The x intercept (where y = 0) is
x = -3/2
17) y = x^2/2 and the slope of the parabola is dy/dx = x
When x = -3, y = 9/2 and the slope is -3. A straight line going through (-3, 9/2) with slope -3 has the equation
y - 9/2 = -3[x -(-3)]
y = -3x + 9/2 -9 = -3x -9/2
The x intercept (where y = 0) is
x = -3/2
There are no AI answers yet. The ability to request AI answers is coming soon!
Submit Your Answer
We prioritize human answers over AI answers.
If you are human, and you can answer this question, please submit your answer.