Answer:
1) The standard form of a circle's equation is (x - h)² + (y - k)² = r². (h,k) is the center and r is the radius.
2) The vertex is the midpoint of the directrix and the focus. It involves the parabola changing directions, and at any point the directrix and the focus will be equidistant from the parabola. The focus is a single point inside the curve of the parabola, and the directrix is a line outside the parabola.
3) The standard form of an equation of an ellipse is:
(x − h)2a 2 +( y − k) 2 b 2 = 1 ( x − h ) 2 a 2 + ( y − k ) 2 b 2 = 1. (h,k) is the center, a is the distance from the center to the horizontal vertices and b is the distance from the center to the vertical vertices.
4) The foci are (−c,0) and (c,0). The ellipse is the set of all points (x,y) which are the sum of the distances from (x,y) to the foci is constant. (a,0) is a vertex of the ellipse. Finally, the endpoints of the minor axis is a co-vertex of the ellipse.
5) A hyperbola has two standard equations. These equations of a hyperbola are based on its transverse axis and conjugate axis. The standard equation of the hyperbola is [(x² / a²) – (y² / b²)] = 1, where the X-axis is the transverse axis and the Y-axis is the conjugate axis.
6) The foci are located on the line that where the transverse axis is. The conjugate axis is perpendicular to the transverse axis and has the co-vertices as its endpoints. The center of a hyperbola is the midpoint of both the transverse and conjugate axes, where they intersect.
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Explanation: