Conic Sections

Two coast guards stations are located $550 \mathrm{km}$ apart at points $A\left(0,0\right)$ and $B\left(0,550\right)$. A distress signal from a ship at $P$ is received at slightly different times by two stations. It is determined that the ship is $200 \mathrm{km}$ farther from station $A$ than it is from station $B$. Determine the equation of hyperbola that passes through the location of the ship.

Two coast guards stations are located $650 \mathrm{km}$ apart at points $A\left(0,0\right)$ and $B\left(0,650\right)$. A distress signal from a ship at $P$ is received at slightly different times by two stations. It is determined that the ship is $200 \mathrm{km}$ farther from station $A$ than it is from station $B$. Determine the equation of hyperbola that passes through the location of the ship.

Two coast guards stations are located $500 \mathrm{km}$ apart at points $A\left(0,0\right)$ and $B\left(0,500\right)$. A distress signal from a ship at $P$ is received at slightly different times by two stations. It is determined that the ship is $200 \mathrm{km}$ farther from station $A$ than it is from station $B$. Determine the equation of hyperbola that passes through the location of the ship.

Two coast guards stations are located $700 \mathrm{km}$ apart at points $A\left(0,0\right)$ and $B\left(0,700\right)$. A distress signal from a ship at $P$ is received at slightly different times by two stations. It is determined that the ship is $200 \mathrm{km}$ farther from station $A$ than it is from station $B$. Determine the equation of hyperbola that passes through the location of the ship.

Two coast guards stations are located $600 \mathrm{km}$ apart at points $A\left(0,0\right)$ and $B\left(0,600\right)$. A distress signal from a ship at $P$ is received at slightly different times by two stations. It is determined that the ship is $200 \mathrm{km}$ farther from station $A$ than it is from station $B$. Determine the equation of hyperbola that passes through the location of the ship.

The equation $y=\frac{1}{20}{x}^2$ models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola, how high is this tube located above the vertex of the parabola?

The equation $y=\frac{1}{40}{x}^2$ models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola, how high is this tube located above the vertex of the parabola?

The equation $y=\frac{1}{16}{x}^2$ models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola, how high is this tube located above the vertex of the parabola?

The equation $y=\frac{1}{32}{x}^2$ models cross sections of parabolic mirrors that are used for solar energy. There is a heating tube located at the focus of each parabola, how high is this tube located above the vertex of the parabola?

A room $28 \mathrm{m}$ long is constructed to be a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is $8 \mathrm{m}$ determine where the foci are located.

A room $30 \mathrm{m}$ long is constructed to be a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is $8 \mathrm{m}$ determine where the foci are located.

A room $36 \mathrm{m}$ long is constructed to be a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is $8 \mathrm{m}$ determine where the foci are located.

A room $32 \mathrm{m}$ long is constructed to be a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is $8 \mathrm{m}$ determine where the foci are located.

A room $34 \mathrm{m}$ long is constructed to be a whispering gallery. The room has an elliptical ceiling, as shown in figure. If the maximum height of the ceiling is $8 \mathrm{m}$ determine where the foci are located.

A concrete bridge is designed as a parabolic arch. The road over bridge is $40 \mathrm{m}$ long and the maximum height of the arch is $13 \mathrm{m}$. Write the equation of the parabolic arch.

A concrete bridge is designed as a parabolic arch. The road over bridge is $40 \mathrm{m}$ long and the maximum height of the arch is $14 \mathrm{m}$. Write the equation of the parabolic arch.

A concrete bridge is designed as a parabolic arch. The road over bridge is $40 \mathrm{m}$ long and the maximum height of the arch is $10 \mathrm{m}$. Write the equation of the parabolic arch.

A concrete bridge is designed as a parabolic arch. The road over bridge is $60 \mathrm{m}$ long and the maximum height of the arch is $20 \mathrm{m}$. Write the equation of the parabolic arch.

A concrete bridge is designed as a parabolic arch. The road over bridge is $40 \mathrm{m}$ long and the maximum height of the arch is $15 \mathrm{m}$. Write the equation of the parabolic arch.

Find the equations of tangents to the hyperbola $\frac{x^2}{4}-\frac{y^2}{8}=1$ which are parallel to $10x-3y+9=0$.