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Chapter 13: Q. 23 (page 526)

Write an equation of the circle that has the given center and radius.

C(鈭�4,鈭�7)鈥夆赌夆赌�;鈥夆赌夆赌�r=5.

Short Answer

Expert verified

The equation of the circle isx+42+y+72=25

Step by step solution

01

Step-1 – Given

The given center = C(-4, -7) and radius = r = 5.

02

Step-2 – To determine

We have to find the equation of the circle.

03

Step-3 – Calculation 

Given that center = (a, b) = (-4, -7) and radius = r = 5.

We will plug them in the standard form of a circle formula to get the equation:

x鈭�a2+y鈭�b2=r2

x鈭�鈭�42+y鈭�鈭�72=52x+42+y+72=25

So, the equation of the circle isx+42+y+72=25.

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Most popular questions from this chapter

In Exercises 28 and 29,

(a) find the lengths of the sides of triangle RST,

(b) use the converse of the Pythagorean Theorem to show that triangle RST is a right triangle, and

(c) find the product of the slopes of RT and ST.

29. R(4, 3), S(-3, 6), T(2, 1)

In Exercises 27-32 find and then compare lengths of segments.

The vertices of triangle KAT and triangle JES are K(3, -1), A(2, 6), T(5, 1), I(-4, 1), E(-3, -6), and S(-6, -1). What word best describes the relationship between triangle KAT and triangle IES?

In Exercises 16-19 a point P on a line and the slope of the line are given. Sketch the line and find the coordinates of two other points on the line.

P(2, 4); slope =鈭�32.

Find the slope of the line through the points named. If the slope is not defined, write not defined.

(1, 2); (-2, -5)

In Exercises 27-32 find and then compare lengths of segments.

Quadrilateral TAUL has vertices T(4, 6), A(6, -4), U(~4, -2), and L(-2, 4), Show that the diagonals are congruent.
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