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Magazine Problem 1
Fill in the blank. A curve obtained by intersecting a double right circular cone and a plane is a(n) __________
Problem 1
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$x^{2}+y^{2}+6 x-3 y+1=0$$
Problem 1
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{6}{1-2 \cos \theta}$$
Problem 2
Fill in the blank. The set of all points in the plane that are equidistant from a fixed line and a fixed point not on the line is a(n) ______________
Problem 2
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$x^{2}-y^{2}+8 x+6 y+2=0$$
Problem 2
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{3}{1-5 \sin \theta}$$
Problem 3
Find the eccentricity and use it to identify each conic as a parabola, ellipse, or hyperbola. Also find the distance between the focus and directrix. $$r=\frac{3}{4-4 \sin \theta}$$
Problem 3
Use completing the square to rewrite the equation in one of the standard forms for a conic and identify the conic. $$2 x^{2}+6 y^{2}+4 x-12 y-3=0$$
Problem 3
Fill in the blank. The set of all points in a plane such that their distance from a fixed point is a constant is \(a(n)\) ___.
Problem 3
Fill in the blank. The ________ of a parabola is the line perpendicular to the directrix and containing the focus.
