How to Find the Equation of a Parabola with Focus (-1, 2) and Directrix x = -5

TL;DR

Find the equation of a parabola given focus and directrix points in a step-by-step process.

Transcript

hi in this problem we're going to try to find the equation of the parabola and we're given some information we're told the focus is negative one comma two and the directrix is x equals negative five let's go ahead and try to solve this solution so i like to do these problems by drawing a little picture so this is the y-axis and this will be the x-a... Read More

Key Insights

• 🆘 Plotting the focus and directrix helps visualize the parabola's orientation.
• 🛟 The vertex serves as the midpoint between the focus and the directrix.
• 🟨 Equations of parabolas vary based on opening direction, either x being squared or y being squared.
• 😀 Sign of c depends on the direction of the parabola's opening.
• 😀 Remember the formula structure: y-k^2 = 4c(x-h) for this problem.
• ❓ Ensure proper substitution of values to reach the final parabolic equation.
• 🤗 Parabolas always open toward their focus point.

Questions & Answers

Q: How do you find the vertex of a parabola with given focus and directrix?

To find the vertex, calculate the midpoint between the focus and the directrix on the axis perpendicular to the directrix.

Q: What formula is used to determine the equation of a parabola in this context?

The formula y-k^2 = 4c(x-h) is employed in this scenario, where c is the distance from the vertex to the focus.

Q: Why does the equation include a squared term for y rather than x?

The parabola opens left or right because the given focus and directrix information dictates that the y term should be squared in this case.

Q: How is the value of c determined in the equation of the parabola?

The absolute value of c is the distance from the vertex to the focus, and its sign depends on the direction of the opening of the parabola.

Summary & Key Takeaways

• Given focus (-1, 2) and directrix x = -5, determine the vertex and equation of the parabola.

• Plot the focus and directrix to find the vertex as the midpoint.

• Use the formula y-k^2 = 4c(x-h) to plug in values and solve for the final equation y-2^2 = 8(x+3).