Explanation Given information: The equation of the circle is x 2 + y 2 − 10 x + 4 y + 20 = 0 Explanation: The standard form of an equation of a circle with the radius r and center ( h , k ) is ( x − h ) 2 + ( y − k ) 2 = r 2 To find the center and the radius of the circle, rewrite the given equation x 2 + y 2 − 10 x + 4 y + 20 = 0 in the standard form Group the terms involving x and terms involving y separately and put the constant on the right side of the equation. ( x 2 − 10 x ) + ( y 2 + 4 y ) = − 20 Complete the square of each expression in parenthesis, note that any number added to the left side must be added on right side also. Constant number should be added in the first parenthesis is ( 1 2 × middle term ) 2 = ( 1 2 × - 10 ) 2 = 25 . Constant number should be added in the second parenthesis is ( 1 2 × 4 ) 2 = 4 Therefore, add 25 in the first parenthesis, 4 in the second parenthesis, and add 25 and 4 on the right side of the equation

10th Edition

ISBN: 9780321979070

Author: Michael Sullivan

Publisher: PEARSON

See similar textbooks

Question

Chapter 3.3, Problem 103AYU

To determine

The center and the radius of the circle x2+y2−10x+4y+20=0

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 3.3, Problem 102AYU

Chapter 3.3, Problem 104AYU

Students have asked these similar questions

The graph below is the function f(z) 4 3 -2 -1 -1 1 2 3 -3 Consider the function f whose graph is given above. (A) Find the following. If a function value is undefined, enter "undefined". If a limit does not exist, enter "DNE". If a limit can be represented by -∞o or ∞o, then do so. lim f(z) +3 lim f(z) 1-1 lim f(z) f(1) = 2 = -4 = undefined lim f(z) 1 2-1 lim f(z): 2-1+ lim f(x) 2+1 -00 = -2 = DNE f(-1) = -2 lim f(z) = -2 1-4 lim f(z) 2-4° 00 f'(0) f'(2) = = (B) List the value(s) of x for which f(x) is discontinuous. Then list the value(s) of x for which f(x) is left- continuous or right-continuous. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5). If there are none, enter "none". Discontinuous at z = Left-continuous at x = Invalid use of a comma.syntax incomplete. Right-continuous at z = Invalid use of a comma.syntax incomplete. (C) List the value(s) of x for which f(x) is non-differentiable. Enter your answer as a comma-separated list, if needed (eg. -2, 3, 5).…

A graph of the function f is given below: Study the graph of f at the value given below. Select each of the following that applies for the value a = -4. f is defined at = a. f is not defined at 2 = a. If is continuous at x = a. Of is discontinuous at x = a. Of is smooth at x = a. f is not smooth at x = a. If has a horizontal tangent line at x = a. f has a vertical tangent line at x = a. Of has a oblique/slanted tangent line at x = a. Of has no tangent line at x = a. f(a + h) − f(a) h lim is finite. h→0 f(a + h) - f(a) lim is infinite. h→0 h f(a + h) - f(a) lim does not exist. h→0 h f'(a) is defined. f'(a) is undefined. If is differentiable at x = a. If is not differentiable at x = a.

Find the point of diminishing returns (x,y) for the function R(X), where R(x) represents revenue (in thousands of dollars) and x represents the amount spent on advertising (in thousands of dollars). R(x) = 10,000-x3 + 42x² + 700x, 0≤x≤20

Chapter 3 Solutions

Precalculus (10th Edition)

Ch. 3.1 - Graph y=x21 Ch. 3.1 - Find the slope of the line joining the points (...Ch. 3.1 - Prob. 3AYU Ch. 3.1 - Solve: 6x900=15x+2850 . (pp. A44-A46)Ch. 3.1 - Prob. 5AYU Ch. 3.1 - Prob. 6AYU Ch. 3.1 - For the graph of the linear function f( x )=mx+b ,...Ch. 3.1 - If the slope m of the graph of a linear function...Ch. 3.1 - True or False The slope of a nonvertical line is...Ch. 3.1 - True or False The average rate of change of f( x...

Knowledge Booster

The center and the radius of the circle x 2 + y 2 − 10 x + 4 y + 20 = 0

Solution Summary: The author explains the standard form of an equation of a circle with the radius and center r.

The center and the radius of the circle x2+y2−10x+4y+20=0

Want to see the full answer?

Chapter 3 Solutions