Find the equation for the parabola that has its vertex at the origin and the focal point is
162 units to the right of the directrix.
equation is
Check Answer

Question

Find the equation for the parabola that has its vertex at the origin and the focal point is 162 units to the right of the directrix. equation is Check Answer

UpStudy AI · Accepted Answer

To find the equation of a parabola with its vertex at the origin and a focal point located 162 units to the right of the directrix, we can follow these steps:

1. **Identify the orientation of the parabola**: Since the focal point is to the right of the directrix, the parabola opens to the right.

2. **Determine the distance from the vertex to the focus**: The distance from the vertex to the focus (denoted as $$ p $$) is 162 units.

3. **Write the standard form of the equation**: For a parabola that opens to the right, the standard form of the equation is given by:
   $$
   y^2 = 4px
   $$
   where $$ p $$ is the distance from the vertex to the focus.

4. **Substitute the value of $$ p $$**: Here, $$ p = 162 $$.

Now, let's substitute $$ p $$ into the equation:

$$
y^2 = 4 \cdot 162 \cdot x
$$

Now, let's calculate $$ 4 \cdot 162 $$:
Calculate the value by following steps:
- step0: Calculate:
  $$4\times 162$$
- step1: Multiply the numbers:
  $$648$$
Now that we have calculated $$ 4 \cdot 162 = 648 $$, we can write the equation of the parabola:

$$
y^2 = 648x
$$

This is the equation for the parabola with its vertex at the origin and the focal point 162 units to the right of the directrix.
The equation of the parabola is $$ y^2 = 648x $$.

Find the equation for the parabola that has its vertex at the origin and the focal point is
162 units to the right of the directrix.
equation is
Check Answer

Upstudy AI Solution

Answer

Solution

Extra Insights

Related Questions

Latest Geometry Questions