( x 1) 2 + ( y 3) 2 = 25

Transcription

1 The locus of points 2 units from the x-axis. The question does not specify the direction of the 2 units so we must include all options. Therefore, the locus of points 2 units from the x-axis is a pair of horizontal parallel lines, one is 2 units above the x-axis at y=2, the other is 2 units below the x-axis at y=-2. The locus of points from a given point is a circle. The locus of points equidistant from two points is the line that joins the intersection of the two circles. In this case, x=-2.

2 The locus of points 5 units from the y-axis is a line parallel to the y-axis. 5 units to the left of the y- axis is -5, so the locus would be a vertical line at x = -5. The locus of points from a given point is a circle. The locus of points equidistant from two points is the line that joins the intersection of the two circles. In this case, y = -1.

3 The locus of points 5 units from the point (1,3) is a circle with its center at (1, 3) and a radius of 5. It's equation would be ( x 1) 2 + ( y 3) 2 = 25 from two intersecting lines is the angle bisector of the angle formed by the intersecting lines. In this case the line x = 0, and y=4 are the bisectors of the intersecting lines.

4 from two intersecting lines is the angle bisector of the angle formed by the intersecting lines. In this case the line x = 2, and y=3 are the bisectors of the intersecting lines. The locus of points from a given point is a circle. The locus of points equidistant from two points is the line that joins the intersection of the two circles. In this case, y = 1.

5 The locus of points 4 units from y=6. The question does not specify the direction of the 4 units so we must include all options. Therefore, the locus of points 4 units from y = 6 is a pair of horizontal parallel lines, one is 4 units above y = 6 at y=10, the other is 4 units below y = 6 at y = 2. from the lines y = 6 and y = 2 has to be a single line parallel to both given lines that runs between them. If you put it above the top line or below the bottom line it will not be the same distance from both lines. The only place that satifies both conditions is directly between the lines. In this case, that is at y = 4.

6 from two intersecting lines is the angle bisector of the angle formed by the intersecting lines. In this case the line y = -x+3, and y = x-3 are the bisectors of the intersecting lines. from the lines y = -x+1 and y = -x+5 has to be a single line parallel to both given lines that runs between them. If you put it above the top line or below the bottom line it will not be the same distance from both lines. The only place that satifies both conditions is directly between the lines. In this case, that is at y = -x+3

7 from two intersecting lines is the angle bisector of the angle formed by the intersecting lines. In this case the line y = 0, and x = 1 are the bisectors of the intersecting lines.

8 In each part of this question they are asking for the locus of points a certain distance from a given point, which is a circle. You need to write the equation of the circle for each given center and radius. ( x 1) 2 + ( y + 4) 2 =16 x 2 + y 2 = 36 x 2 + ( y 1) 2 = 9 ( x +1) 2 + y 2 =1 x 2 + ( y 2) 2 = 6.25 ( x +1) 2 + ( y 3) 2 = The showers should be placed 35 feet from each diving board. If the pools are 70 feet apart 35 feet would be exactly halfway between each pool.