1. A piece of broken plate was dug up in an archaeological site. It was put on top a grid with the arc of the plate passing through A (-7, 0), B(1,4) and C(7,2). Find its center, and the standard equation of circle describing the boundary of the plate.
Direction: For each problem, draw a picture on a Cartesian coordinate plane, clearly showing
important points. Then, write an equation and use it to answer each question. Provide/show
necessary solutions.
1. A piece of broken plate was dug up in an archaeological site. It was put on top a grid with the
arc of the plate passing through A (-7, 0), B(1,4) and C(7,2). Find its center, and the standard
equation of
2. A seismological station is located at (0, -3), 3 km away from a straight shoreline where the axis
runs through. The epicentre of an earthquake was determined to be 6km away from the
station.
a) Find the equation of the curve that contains the possible location of epicenter.
b) If furthermore, the epicenter was determined to be 2 km away from the shore, find its
possible coordinates (rounded off to two decimal places).
3. According to Kepler’s Law, planets have elliptical orbits, with the sun at one of the foci. The
farthest Pluto gets from the sun is 7.4 billion kilometers. The closest it gets to the sun is 4.4
billion kilometers. Find the equation of Pluto’s orbit assuming a center at (0,0).
4. A satellite dish has a shape called a paraboloid, where each cross-section is a parabola. Since
radio signals (parallel to the axis) will bounce off the surface of the dish to the focus, the
receiver should be place at the focus. How far should the receiver be from the vertex, if the
dish is 14ft across, and 6.5ft deep at the vertex?
5. An explosion is heard by two stations 1200 m apart, located at F1 (-600, 0) F2 (600,
0). If the explosion was heard in F1 two seconds before it was heard in F2, identify the possible
locations of the explosion. Use 340 m/s as the speed of the sound.
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