SAT Math assist » Geometry » name: coordinates Geometry » circles » just how to discover the equation of a circle

A circle has actually a center at (5,5) and also a radius the 2. If the layout of the equation for the one is (x+A)2+(y+B)2=C, what is C?


Explanation:

The circle has a facility at (5,5) and also a radius that 2. Therefore, the equation is (x+5)2+(y+5)2=22, or (x+5)2+(y+5)2=4. 


If the facility of a circle is in ~ (0,4) and also the diameter that the circle is 6, what is the equation of the circle?


Explanation:

The formula for the equation that a circle is:

(x-h) 2 + (y-k)2 = r2

Where (h,k) is the facility of the circle.

You are watching: A circle has its center at (−1, 2) and a radius of 3 units. what is the equation of the circle?

h = 0 and also k = 4

and diameter = 6 because of this radius = 3

(x-0) 2 + (y-4)2 = 32

x2 + (y-4)2 = 9


Circle A is offered by the equation (x – 4)2 + (y + 3)2 = 29. One A is change up five units and also left by six units. Then, the radius is doubled. What is the brand-new equation for circle A?


Explanation:

The general equation that a one is (x – h)2 + (y – k)2 = r2, where (h, k) represents the place of the circle\"s center, and r represents the size of that radius. 

Circle A first has the equation of (x – 4)2 + (y + 3)2 = 29. This way that its center must be situated at (4, –3), and its radius is √29.

We room then told that circle A is shifted up 5 units and then left by six units. This way that the y-coordinate the the facility would increase by five, and also the x-coordinate of the facility would diminish by 6. Thus, the brand-new center would be located at (4 – 6, –3 + 5), or (–2, 2).

We room then told that the radius of circle A is doubled, which way its new radius is 2√29.

Now, the we have circle A\"s brand-new center and radius, we have the right to write its general equation using (x – h)2 + (y – k)2 = r2.

(x – (–2))2 + (y – 2)2 = (2√29)2 = 22(√29)2 = 4(29) = 116.

(x + 2)2 + (y – 2)2 = 116.

The price is (x + 2)2 + (y – 2)2 = 116.


Report an Error

Example inquiry #1 : just how To discover The Equation of A circle


Which the the following equations explains all the point out (x, y) in a coordinate aircraft that are 5 units far from the allude (–3, 6)?


Possible Answers:

(x – 3)2 – (y + 6)2 = 25


(x – 3)2 + (y + 6)2 = 5


(x – 3)2 + (y + 6)2 = 25


y + 6 = 5 – (x – 3)2


(x + 3)2 + (y – 6)2 = 25


Correct answer:

(x + 3)2 + (y – 6)2 = 25


Explanation:

We space trying to discover an equation for all of the point out that room the exact same distance (5 units) from (–3, 6). The locus of every points equidistant native a solitary point is a circle. In various other words, we require to uncover an equation that a circle. The facility of the circle will be (–3, 6), and the radius, i beg your pardon is the distance from (–3,6), will certainly be 5. 

The standard type of a one is given below:

(x – h)2 + (y – k)2 = r2, wherein the facility is situated at (h, k) and r is the length of the radius.

In this case, h will certainly be –3, k will be 6, and also r will certainly be 5.

(x – (–3))2 + (y – 6)2 = 52

(x + 3)2 + (y – 6)2 = 25

The price is (x + 3)2 + (y – 6)2 = 25.


Report one Error

Example concern #1 : how To discover The Equation that A one


What is the equation for a circle of radius 12, focused at the intersection of the two lines:

y1 = 4x + 3

and

y2 = 5x + 44?


Possible Answers:

(x + 41)2 + (y + 161)2 = 144


(x - 22)2 + (y - 3)2 = 12


(x - 41)2 + (y - 161)2 = 144


None of the various other answers


(x - 3)2 + (y - 44)2 = 144


Correct answer:

(x + 41)2 + (y + 161)2 = 144


Explanation:

To begin, let us determine the suggest of intersection of these 2 lines by setup the equations equal to every other:

4x + 3 = 5x + 44; 3 = x + 44; –41 = x

To uncover the y-coordinate, substitute into one that the equations. Let\"s use y1:

y = 4 * –41 + 3 = –164 + 3 = –161

The center of ours circle is therefore: (–41, –161).

Now, recall the the general kind for a one with facility at (x0, y0) is:

(x - x0)2 + (y - y0)2 = r2

For our data, this means that our equation is:

(x + 41)2 + (y + 161)2 = 122 or (x + 41)2 + (y + 161)2 = 144


Report an Error

Example question #1 : exactly how To find The Equation of A circle


The diameter the a circle has actually endpoints in ~ points (2, 10) and also (–8, –14). Which of the complying with points does not lie top top the circle?


Possible Answers:

(–8, 10)


(–8,–12)


(9,3)


(–15, –7)


(2, –14)


Correct answer:

(–8,–12)


Explanation:

\"*\"

 

\"*\"


Report an Error

Example inquiry #1 : how To find The Equation the A circle


A circle exists completely in the an initial quadrant such the it intersects the

\"*\"
-axis in ~
\"*\"
. If the circle intersects the
\"*\"
-axis in at least one point, what is the area that the circle?


Possible Answers:

\"*\"


\"*\"


\"*\"


\"*\"



Correct answer:


Explanation:

We are given two really important pieces of information. The very first is the the one exists completely in the an initial quadrant, the 2nd is that it intersects both the

\"*\"
- and
\"*\"
-axis. 

The truth that it is totally in the an initial quadrant way that it can not go past the two axes. Because that a circle to crossing the

\"*\"
-axis in much more than one point, it would necessarily relocate into another quadrant. Therefore, we have the right to conclude it intersects in specifically one point.

The intersection that the circle with 

\"*\"
must also be tangential, since it have the right to only crossing in one point. We can thus conclude the the circle must have both
\"*\"
- and
\"*\"
- intercepts equal to 6 and have a center of
\"*\"
.

This leaves us through a radius of 6 and also an area of:

\"*\"


Report an Error

Example concern #1 : just how To uncover The Equation the A one


We have actually a square with size 2 sitting in the an initial quadrant through one corner touching the origin. If the square is inscribed within a circle, find the equation of the circle.


Possible Answers:
Correct answer:

\"*\"


Explanation:

If the square is inscribed within the circle, in means the facility of the circle is at (1,1). We require to also find the radius the the circle, which wake up to be the size from the corner of the square come it\"s center.

\"*\"

Now usage the equation of the circle v the center and also

\"*\"
.

We get 

\"*\"


Report an Error

Example question #1 : one


What is the radius the a circle with the equation 

\"*\"
?

 


Possible Answers:
Correct answer:

\"*\"


Explanation:

We require to broaden this equation to

\"*\"
 and then finish the square.

This brings us to

\"*\"
.

We leveling this come

\"*\"
.

Thus the radius is 7.


Report one Error

Example inquiry #1 : exactly how To uncover The Equation that A one


A circle has actually its origin at

\"*\"
. The point 
\"*\"
is ~ above the sheet of the circle. What is the radius that the circle?


Possible Answers:

There is not sufficient information to answer this question.


Correct answer:

\"*\"


Explanation:

The radius of the one is equal to the hypotenuse that a ideal triangle v sides the lengths 5 and 7.

\"*\"

\"*\"

\"*\"

This radical can not be reduced further.

See more: M A Downward Shift In The Consumption Function Can Be Caused By:


Report an Error
← vault 1 2 3 4 next →
watch SAT mathematics Tutors
Liban Certified tutor
Emory University, Bachelor the Science, Mathematics/Economics.
view SAT mathematics Tutors
Humberto Certified tutor
The university of Texas in ~ Austin, Bachelors, Mathematics. University of Saint thomas , Masters, Education.
watch SAT math Tutors
Jeffrey Certified tutor
Lyndon State College, Bachelor of Science, science Teacher Education. East Connecticut State University, grasp of Arts, E...

All satellite Math sources


16 Diagnostic exam 660 exercise Tests inquiry of the job Flashcards find out by concept
SAT mathematics Tutoring in optimal Cities:
Atlanta satellite Math Tutoring, Austin sat Math Tutoring, Boston satellite Math Tutoring, Chicago sat Math Tutoring, Dallas fort Worth sat Math Tutoring, Denver sat Math Tutoring, Houston sat Math Tutoring, Kansas City satellite Math Tutoring, Los Angeles satellite Math Tutoring, Miami satellite Math Tutoring, brand-new York City satellite Math Tutoring, Philadelphia sat Math Tutoring, Phoenix sat Math Tutoring, mountain Diego satellite Math Tutoring, mountain Francisco-Bay Area satellite Math Tutoring, Seattle sat Math Tutoring, St. Louis satellite Math Tutoring, Tucson satellite Math Tutoring, Washington DC sat Math Tutoring
SAT mathematics Tutors in optimal Cities:
Atlanta sat Math Tutors, Austin sat Math Tutors, Boston satellite Math Tutors, Chicago sat Math Tutors, Dallas fort Worth sat Math Tutors, Denver satellite Math Tutors, Houston satellite Math Tutors, Kansas City satellite Math Tutors, Los Angeles satellite Math Tutors, Miami sat Math Tutors, new York City sat Math Tutors, Philadelphia satellite Math Tutors, Phoenix sat Math Tutors, mountain Diego sat Math Tutors, mountain Francisco-Bay Area satellite Math Tutors, Seattle sat Math Tutors, St. Louis satellite Math Tutors, Tucson satellite Math Tutors, Washington DC satellite Math Tutors
Popular process & Classes
LSAT process & class in Miami, ISEE process & great in Boston, Spanish courses & great in Phoenix, LSAT courses & class in mountain Diego, MCAT process & classes in san Diego, Spanish courses & classes in Houston, MCAT process & great in Chicago, GRE process & class in Seattle, GMAT process & great in Phoenix, Spanish courses & great in san Diego
Popular test Prep
ISEE test Prep in Boston, ACT test Prep in mountain Francisco-Bay Area, GRE check Prep in Los Angeles, ACT test Prep in Washington DC, LSAT check Prep in Atlanta, ISEE test Prep in Chicago, MCAT check Prep in Seattle, MCAT test Prep in brand-new York City, ACT test Prep in Dallas fort Worth, sat Test prepare in Miami
Report an concern with this question

If you\"ve discovered an worry with this question, you re welcome let us know. V the assist of the ar we can proceed to boost our education resources.


Do not fill in this field
* your Name:
* issue Description:
DMCA complaint

your Infringement notification may it is in forwarded to the party that made the content easily accessible or to 3rd parties such together ChillingEffects.org.

please follow these steps to document a notice:

you must incorporate the following:

Send your complain to ours designated certified dealer at:

Charles Cohn Varsity Tutors llc 101 S. Hanley Rd, Suite 300 St. Louis, MO 63105