Find the equation of a circle with a center at (–7, –1) where a point on the circle is (–4, 3).
1 answer:
Answer:
(x + 7)^2 + (y + 1)^2 = 25.
Step-by-step explanation:
The center of a circle is easy to set up. According to the formula below, the formula for the circle will be (x - a)^2 + (y - b)^2 = r^2.
In this case, a = -7 and b = -1, so we have...
(x - (-7))^2 + (y - (-1))^2 = r^2
(x + 7)^2 + (y + 1)^2 = r^2
To get the radius, we need to find the distance between the center and the point on the circle. The distance formula is d = sqrt((x2 - x1)^2 + (y2 - y1)^2).
In this case, x2 = -4, x1 = -7, y2 = 3, and y1 = -1.
sqrt((-4 - -7)^2 + (3 - -1)^2) = sqrt((-4 + 7)^2 + (3 + 1)^2) = sqrt((3)^2 + (4)^2) = sqrt(9 + 16) = sqrt(25) = plus or minus 5.
Since distance can only be positive, the distance is 5 units, meaning that the radius is 5 units.
5^2 = 25
So, your equation should be (x + 7)^2 + (y + 1)^2 = 25.
Hope this helps!
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Answer:
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Step-by-step explanation:
I've attached an image showing the coordinates of Ship A and Ship B.
Answer:
distressed vessel is located at (1, 1.5)
Step-by-step explanation:
From the image attached, we can see that;
Coordinate of ship A is (3, 4)
Coordinate of ship B is (1, 1)
Now, we are told that Ship A receives a distress signal from the southwest, and ship B receives a distress from the same vessel from the north.
This means that the distressed ship is somewhere in between ship A & B.
To solve this, we will extend the arrow line from Ship A in that same SW direction and we will do the same for ship B in the same North direction. Their point of intersection is where the distressed ship is located.
Now, if we do that, we will see that they will intersect at the point; (1, 1.5)
Thus,distressed vessel is located at (1, 1.5)
