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Chapter 10: Q 9. (page 643)

Answer Problem using the figure.

If a = 4, then the coordinates of the focus are___________.

Short Answer

Expert verified

If a = 4, then the coordinates of the focus are (3, 6).

Step by step solution

01

Step 1. Given information.

We have given graph is,

02

Step 2. Concept used.

Focus of the parabola:

A parabola represents the locus of a point that is equidistant from a fixed point called the focus .

and coordinates of the focus of the upward parabola is: (h,k+a)

Where (h,k) is the vertex of the parabola.

03

Step 3. Explanation

From the given figure of the parabola we have coordinates of the vertex of parabola is (3, 2).

Comparing it with (h,k) we will get,

h = 3 and k = 2 and we have a = 4

So coordinates of the focus of the parabola is

(h,k+a) = (3, 2 + 4) = (3, 6).
04

Step 4. Conclusion.

Hence, coordinates of the focus of the parabola is (3, 6).

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Most popular questions from this chapter

A hyperbola for which a=bis called an equilateral hyperbola. Find the eccentricity eof an equilateral hyperbola.

[Note: The eccentricity of a hyperbola is defined in Problem 81.]

Whispering Gallery: A hall 100feet in length is to be designed as a whispering gallery. If the foci are located 25feet from the center, how high will the ceiling be at the center?

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