Important Geometry Question
Question:An architect designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625y^2 - 400x^2=250,000, where x and y are in yards. How far apart are the houses at their closeset point?
Answers:625y^2 - 400x^2=250,000 y^2 / 20^2 - x^2 / 25^2 = 1 The closest two points on separate branches are the vertices, and their separation is 2 * 20 = 40yd. I find the question a little confusing, though.
Question:LORAN (long distance radio navigation) for aircraft and ships use synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150, 0) and (150, 0) and that a ship is traveling on a path with coordinates (x,75). Find the x-coordinate of the position of the ship if the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 second).
Answers:ok redone it y-186=SQRTt((300-x)^2+75^2), y=(SQRT((x^2+75^2) co-ordinate moves so no negative numbers and is -110.279 or +110.279
Question:The question is to the the standard equation for the hyperbola with the given characterstics. center(1,3) one focus(1,-14) one vertex (1,18) the answer is (y-3)^2/225 - (x-1)^/64=1 Why!? And HOW
Answers:The center is (1,3) because (y-k)^2/a^2-(x-h)^2/b^2=1 is the form of a hyperbola. (h,k) is the center. The denominator is also larger for the fraction with the y variable, so it is a vertical hyperbola. Foci=(h,k+/-c) c=sqrt (a^2+b^2) a^2=225 b^2=64 c=sqrt289 c=-17 or 17 Add c to the y value or the center since this is a vertical hyperbola. (1,3+(-17)=(1,-14) So (1,-14) is one of the foci, the other one is (1,20) Vertex is (1,18) because you add the y value to a a=sqrt 225
Answers:625y^2 - 400x^2=250,000 y^2 / 20^2 - x^2 / 25^2 = 1 The closest two points on separate branches are the vertices, and their separation is 2 * 20 = 40yd. I find the question a little confusing, though.
Question:LORAN (long distance radio navigation) for aircraft and ships use synchronized pulses transmitted by widely separated transmitting stations. These pulses travel at the speed of light (186,000 miles per second). The difference in the times of arrival of these pulses at an aircraft or ship is constant on a hyperbola having the transmitting stations as foci. Assume that two stations, 300 miles apart, are positioned on a rectangular coordinate system at (-150, 0) and (150, 0) and that a ship is traveling on a path with coordinates (x,75). Find the x-coordinate of the position of the ship if the time difference between the pulses from the transmitting stations is 1000 microseconds (0.001 second).
Answers:ok redone it y-186=SQRTt((300-x)^2+75^2), y=(SQRT((x^2+75^2) co-ordinate moves so no negative numbers and is -110.279 or +110.279
Question:The question is to the the standard equation for the hyperbola with the given characterstics. center(1,3) one focus(1,-14) one vertex (1,18) the answer is (y-3)^2/225 - (x-1)^/64=1 Why!? And HOW
Answers:The center is (1,3) because (y-k)^2/a^2-(x-h)^2/b^2=1 is the form of a hyperbola. (h,k) is the center. The denominator is also larger for the fraction with the y variable, so it is a vertical hyperbola. Foci=(h,k+/-c) c=sqrt (a^2+b^2) a^2=225 b^2=64 c=sqrt289 c=-17 or 17 Add c to the y value or the center since this is a vertical hyperbola. (1,3+(-17)=(1,-14) So (1,-14) is one of the foci, the other one is (1,20) Vertex is (1,18) because you add the y value to a a=sqrt 225