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Transcript of math
know the standard form of an ellipse equation Real life Problem A new school is planning to build a field with the shape of an ellipse.
The school is building two goals at the two foci of the field. The
distance between the two goals should be 250 m. The furthest
distance from one end of the field to another end of the field is
going to be 300 m.
Write an equation to model the soccer field
Circle Parabola Hyperbola The distance between two goals
The distance between two foci of the ellipse
How do get the value of foci? For the equation of an ellipse,
this is the formula to get the value of foci: Then, we should consider what information has been given from the question. 1. The distance between two goals is 250 m 2. The furthest distance from one end
to another end is 300 m. The length of the major axis of the equation is 300 We can solve the value of 'a', which is the value of vertices, with the given data. Thus, = 22500 Now, we have the value of 'c' and 'a', so we can solve
for the value of based on the formula of foci. a 2 b 2 Therefore, the equation to model the
soccer field would be: x y 2 2 22500 6875 =1 + Real Life Problem In my bedroom, there is a beautiful parabola lamp just like this picture. The location of the light bulb is at the focus of the lamp. The distance between the light bulb and the end of the lamp is 7 cm.
Set up an equation to model this parabola lamp. Real life problem A park nearby my house is designed as a circle.
There are two public restrooms inside the park.
One is located on the circle, at the point (1,2),
and another is located at the center of the park.
I love you a. If the center of the park is at (3,2) of a graph,
solve for the distance between the two restrooms. b. Set up an equation to model this circular park. *Light bulb is located at the focus of the lamp.
If C is the distance from the vertex to the focus, Based on the information provided by the problem,
Now, we can solve for 'a' When we look at the picture of the lamp,
the parabola is opened upward.
The Standard equation form of an upward-opened parabola is: We know the value of 'a' ,
so we can set up an equation to model this lamp. The distance between two restrooms
Radius of the circle Use distance formula to find the radius. two given points: (1,2) and (3,2) r = 2 Center: (3,2)
Radius : 2 Standard form equation of a circle is: Real Life Problem A spacecraft is exploring around the outmost planet of the solar system, Neptune. The spacecraft travels around the outer orbit, which is in hyperbola form. The distance from the vertex of the hyperbola to the center of the hyperbola is 233,891 km; the distance from Neptune to the center of hyperbola is 334,126 km. The distance from the vertex to the center of the hyperbola
value of vertex (because the center is at the origin)
value of 'a' in the standard equation Set up an equation to model the spacecraft's path, assume that the
center of the hyperbola is at the origin and transverse axis is horizontal the distance from Neptune to the center of hyperbola
value of the focus of hyperbola (c) The value of 'a' and 'c' are given in the problem.
a = 233,891 c = 334,126 Now, we can find the value of 'b' using