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The tow tangents to the curve y equals x2 at the point where y equals 9 intersect at the point p fin d the coordinates of p?
Wiki User
∙ 14y ago
y = x2
y' = 2x (the slope of the tangent line at a point on the curve of y = x2)
Since the graph of the given equation it is a parabola (which has the y-axis as a line of symmetry), let's evaluate the slope of the tangent lines l1 and l2 that pass through the points (-3, 9) and (3, 9).
So that
m1 = 2(-3) = -6
m2 = 2(3) = 6
Use those slopes and the points (-3, 9) and (3, 9) to find the equations of the tangent lines such that
For l1:
(y - 9) = -6(x - -3)
y - 9 = -6x - 18
y = -6x - 9
For l2:
(y - 9) = 6(x - 3)
y - 9 = 6x - 18
y = 6x - 9
Now we have to find the intersection point of the two tangents.
y = -6x - 9
y = 6x - 9 (add both equations)
0 = -12x
0 = x yields y = -9
Thus, the intersection point of the two tangents of the graph of y = x2 at points (-3, 9) and (3, 9) is (0, -9).
Wiki User
∙ 14y ago
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