The radius of a circle is 3 miles. What is the length of a 90° arc?
1 answer:
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Answer:
yes
Step-by-step explanation:
The line intersects each parabola in one point, so is tangent to both.
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For the first parabola, the point of intersection is ...
y^2 = 4(-y-1)
y^2 +4y +4 = 0
(y+2)^2 = 0
y = -2 . . . . . . . . one solution only
x = -(-2)-1 = 1
The point of intersection is (1, -2).
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For the second parabola, the equation is the same, but with x and y interchanged:
x^2 = 4(-x-1)
(x +2)^2 = 0
x = -2, y = 1 . . . . . one point of intersection only
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If the line is not parallel to the axis of symmetry, it is tangent if there is only one point of intersection. Here the line x+y+1=0 is tangent to both y^2=4x and x^2=4y.
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Another way to consider this is to look at the two parabolas as mirror images of each other across the line y=x. The given line is perpendicular to that line of reflection, so if it is tangent to one parabola, it is tangent to both.
A(−3,−2), B(−2,2), C(2,−2)
The orthocenter is the meet of the altitudes. We see AC is parallel to the x axis so the perpendicular is the altitude through B.
Between A and B we have slope (2 - -2)/(-2 - -3) = 4 so perpendicular slope -1/4 through C(2,-2):
For the y coordinate of the orthocenter we substitute in x=-2.
So the orthocenter is (x,y)=(-2,-1)
Answer: (-2,-1)