Answer:
The option in the top right...
Step-by-step explanation:
Answer:
D) a hyperbola
Step-by-step explanation:
IMO, the image is not helpful, as it suggests the ends of the curve are nearly parallel to each other. In fact, the ends of the curve asymptotically approach straight lines parallel to the sides of the cone. That is, there are asymptotes that form an X shape. This is a characteristic of a hyperbola.
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A parabola is formed when the plane cuts the cone parallel to one side. That cut plane only intersects one nap of the cone. At a shallower angle yet, one gets an ellipse. Parallel to a base, one gets a circle.
The Pythagorean Theorem states that for right triangles:
a^2=b^2+c^2
a= the hypotenuse
b and c equals the other two sides.
In this case we are given the hypotenuse so we can rearrange the equation to look like this b^2=a^2-c^2 (I subtracted c^2 from both sides). I know a and c so I can solve for b.
We get rid of a square by implementing a square root on both sides and get:
b=sqrt(a^2-c^2) .... b=sqrt( (sqrt(34))^2 - 3^2)
b= sqrt(25) ..... b=5
