Analytic Geometry Answers

1. A duly-licensed engineer designs two houses that are shaped and positioned like a part of the branches of the hyperbola whose equation is 625𝑦2 − 400𝑥2 = 250,000, where x and y are in yards. How far apart are the houses at

their closest point?

Direction: Using the information given on each item, write the

standard form equation of each ellipse.

1. Vertices: (12, -4), (-14, -4)

Foci: (11, -4), (-13, -4)

2. Vertices: (6,22), (6, -4)

Foci: (6, 14), (6,4)

3. Foci: (0,9), (-10,9)

Co-vertices: (-5, -21), (-5, -3)

4. Foci: (5,-8), (5,-8)

Co-vertices: (0,4), (0, -20) 5. Center: (6, 2)

Vertex: (6, -4) Co-vertex: (9,2)

2. The recently made suspension bridge cables in New Bataan Hydro plant are in the shape of a parabola. The distance between two towers supporting the cable are 800 feet apart and the height is 200 feet. If the vertical support cables are at 100 feet intervals along the level roadway, what are the lengths of these vertical cables?

1. Mrs. Flores recently subscribed in a tv cable plan at GSAT Company. The receiving dish of the GSAT Cable is in the shape of a paraboloid of revolution. Find the location of the receiver which is placed at the focus if the dish is 12 feet across and 3 feet deep.

a certain celestial body is orbiting around a star somewhere in space and astronaut tries to graph out the elliptical orbit of the celestial body using dimensional analysis and scaling in his drawing the celestial body is in origin and he finds out that equation of the elliptical orbit is 4x²+9y²-256x+342y+k=0 for some value of k if is finding are true find the location of the star in the cartesian plane

17x²+7y²=119

Find the equation of the line which passes through the point (9,5

9,5) and has slope 1

1. Give your answer in the form y=m x+b

y=m x+b. The constants should be given exactly, e.g., 1/3 rather than 0.33.

For what values of c are the vectors [−8, 𝑐, 4] and [𝑐, 𝑐 2 , 𝑐] orthogonal?