1. A seismological station is located at (0,-3), 3 km away from a straight shoreline where the x- axis runs through. The epicenter of an earthquake was determined to be 6 km away from the station. Find the equation of the curve that contains the possible location of the epicenter.
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Answer:
x^2 + (y + 3)^2 = 6^2
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Step-by-step explanation:
Given A seismological station is located at (0,-3), 3 km away from a straight shoreline where the x- axis runs through. The epicenter of an earthquake was determined to be 6 km away from the station. Find the equation of the curve that contains the possible location of the epicenter.
- So the formula will be
- (x – h)^2 + (y – k)^2 = r^2
- where centre is (h,k) and r is the radius.
- So centre (h,k) = (0,-3)
- radius r = 6
- Now substituting these in the equation we have
- (x – 0)^2 + (y – (-3))^2 = 6^2
- (x – 0)^2 + (y + 3)^2 = 36
- x^2 + y^2 + 6y + 9 = 36 ( (a + b)^2 = a^2 + 2ab + b^2))
- x^2 + y^2 + 6y + 9 – 36
- x^2 + y^2 + 6y – 27 will be the equation
Reference link will be
https://brainly.ph/question/16862585
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