Analytic Geometry Answers

A semi-elliptical archway over a one-way road has a height of 9 ft and width of 36 ft. Your van has a width of 12 ft and height of 8 ft. Will your van be able to clear the opening of the archway?

Find the equations of the tangent and normal to each of the following conics, the lengths of the subtangent and subnormal, then trace the curve showing these lines.

1. y2 = -9 (x – 3) at (2, 3).
2. 4x2 + 3y2 + 16x + 36y – 68 = 0 at (4, -2)
3. 9x2 – 4y2 – 108x – 56y + 128 = 0 at (0, 2).
4. x2 + y2 – 8x – 6y + 15 = 0 at (5, 0).

Identify the center, vertices, and foci. Then sketch the graph.

((x + 3) ^ 2)/9 + (y ^ 2)/25 = 1

Find the equations of the tangent and normal to each of the following conics, the lengths of the subtangent and subnormal, then trace the curve showing these lines.

y = x2 – 6x + 4 at (4, -4)

find the center,foci,vertices, endpoints of conjugate axis.determine the equation of the asymptotes and sketsch the graph

1. (y+6)²/25-(x-4)²/39=1

2. 9x²+126x-16y²-96y+153=0

Identify the vertex, focus, axis of symmetry, directrix, direction of opening, length of the latus rectum, and the x- and y-intercepts of: 2y ^ 2 + x + 20y + 51 = 0

Use the information provided to write the standard form equation of the parabola.Vertex:(3,4) Focus:(3 ¹⁵/⁴)

Identify the center and radius of x²+y²-8x+6y+16=0.Then sketch the graph.

Find the equation in general form of the circle with center (3,5) and tangent to the x axis.

Two stations, located at M(−1.5, 0) and N(1.5, 0) (units are in km), simultaneously send sound signals to a ship, with the signal traveling at the speed of 0.33 km/s. If the signal from N was received by the ship four seconds before the signal it received from M, find the equation of the curve containing the possible location of the ship.