The standard form of the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h,k) is the center of the circle, (x,y) is a point of the circle, and r is the length of the radius of the circle. When the equation of a circle is written, h,k, and r are numbers, while x and y are still variables. (x-2)^2 + (y-k)^2 = 16 is an example of a circle. The problem gives us two of the three things that a circle has, a point (5,9) and the center (-2,3). We need to find the radius in order to write the equation. We substitute -2 for h, 3 for k, 5 for x, and 9 for y to get (5 - (-2))^2 + (9 - 3)^2 = r^2 We simplify: 49 + 36 = r^2, r^2 = 85. We only need to know r^2 because the equation of a circle has r^2. We now have all the information to write the equation of a circle. (x + 2)^2 + (y - 3)^2 = 85.
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<u><em>Answer:</em></u> s = 22°
<u><em>Explanation:</em></u> <u>1- getting the top right angle of line B:</u> We are given that: the top right angle of line A = 158° Since lines A and B are parallel, therefore, the top right angle of line A and the top right angle of line B are corresponding angles which means that they are equal This means that: <u>Top right angle of line B = 158°</u>
<u>2- getting the value of s:</u> Now, taking a look at line B, we can note that: angle s and the top right angle form a straight angle. This means that the sum of these two angles is 180° Therefore: 180 = s + 158 s = 180 - 158 <u>s = 22°</u>