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Chapter 13: Q. 45 (page 528)

Find the center and the radius of the circlex2+4x+y2鈭�8y=16.

(Hint: Express the given equation in the form

x鈭�a2+y鈭�b2=r2)

Short Answer

Expert verified

The center is (-2, 4) and the radius is 6.

Step by step solution

01

Step-1 – Given

The given equation is: x2+4x+y2鈭�8y=16.

02

Step-2 – To determine

We have to find the center and radius of the given circle.

03

Step-3 – Calculation 

We first write the equation to the standard form of a circle:

x2+4x+y2鈭�8y=16x2+4x+4+y2鈭�8y+16=16+20addbothsides20x2+22x+22+y2鈭�24y+42=36perfectsquaretrinomialx+22+y鈭�42=62

The standard form of a circle is:x鈭�a2+y鈭�b2=r2

Where (a, b) = center and r = radius.

Then we compare the given equation to the standard form of a circle:

a=鈭�2,b=4andr=6.

So, the center is (-2, 4) and the radius is 6.

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Most popular questions from this chapter

In Exercises 20 and 21 show that points P, Q, and R are collinear by showing that PQ and OR have the same slope.

P(-1, 3) Q(2, 7) R(8, 15)

a. Find the slope of AB.

b. Find tan n掳.

c. Consider the statement: If a line with positive slope makes an acute angle of n掳 with the x-axis, then the slope of the line is tan n掳. Do you think this statement is true or false? Explain.

10. Find the distance between the points named. Give all answers in simplest

form.

  1. (0, 0) and (5, -3).
  2. (3, -2) and (-5, -2).

3. (4, 4) and (-3, -3).

Find the slope and length of AB.

A(3, -1), B(5, -7)

a. Show that tan鈭燗 = slope of AC.

b. Use trigonometry to find m鈭燗.
See all solutions

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