posted 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)
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