A circle touches the lines 5x + 2y - 10 = 0 and 5x + 2y + 2 = 0. Find its area and locus of its center.
Thank You...
2007-10-03 08:33:47 · 3 answers · asked by sweet_candy 2 in Science & Mathematics ➔ Mathematics
The locus of the center of the circle is is a line parallel to and equidistant from the two given lines. Its equation is
5x +2y = 4.
The distance between the two || lines is the distance from the point(0,5) to the line 5x+2y +2 = 0 annd is given by:
d = |ax1+by1 +c|/(sqrt(a^2+b^2)
d= |5*0 + 2*5 +2|/sqrt(5^2+2^2)
d = 12/sqrt(29)
A = pi d^2/4 = 144pi/(29*4) = 36pi/29
2007-10-03 08:57:54 · answer #1 · answered by ironduke8159 7 · 1⤊ 0⤋
The two lines are parallel, so the radius can be calculated as half the distance between the two lines.
5x + 2y - 10 = 0
5x + 2y + 2 = 0
Pick a point on one line and calculate the distance to the other line. Select the point on the first line P(2, 0). The distance from P to the second line is calculated as:
distance = |5*2 + 2*0 + 2| / √(5² + 2²)
distance = 12/√29
radius = (1/2)(12/√29) = 6/√29
The area of the circle is
πr² = π(6/√29)² = 36π/29
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The locus of the center of the circle is the line that is parallel to the two given lines and midway between them. Its equation is:
5x + 2y + (-10 + 2)/2 = 0
5x + 2y - 4 = 0
2007-10-04 10:22:45 · answer #2 · answered by Northstar 7 · 1⤊ 0⤋
you're nicely suited - the slope of this line is 5/2. So the slope of a perpendicular line is -2/5. This passes by using (0,0) so it has 0 intercept. The equation for that's y=(-2/5)x + 0 or 5y + 2x = 0.
2016-12-28 13:09:57 · answer #3 · answered by ? 4 · 0⤊ 0⤋