Maths-

General

Easy

Question

# x^{2 }+ 20x + y^{2 }+ 16y = -20

The equation above defines a circle in the *xy*-plane. What are the coordinates of the center of the circle?

- (−20, −16 )
- (−10, −8)
- (10, 8)
- (20, 16)

## The correct answer is: (−10, −8)

### The standard equation of a circle is given by:

(x-h)^{2} + (y-k)^{2} = r^{2}

Where (h,k) is the coordinates of center of the circle and r is the radius.

- We know that,

The standard equation of a circle in the *xy*-plane is of the form

(*x *− *h*)^{2} + (*y *− *k*)^{2} = *r*^{2} , where (*h*, *k*) are the coordinates of the center of the circle and *r *is the radius.

- We are given a equation of circle in xy plane ,

x^{2 }+ 20x + y^{2 }+ 16y = -20

- To convert the given equation to the standard form, first complete the squares. To do this we have to find the values which will be added to then complete the square .
- The first two terms need a 100 to complete the square, and the second two terms need a 64.
- Adding 100 and 64 to both sides of the given equation

(x^{2 }+ 20x +100) +(y^{2 }+ 16y+64) = -20+100+64

We can see first bracket is equivalent to (x+10)^{2} and second bracket is equivalent to (y+8)^{2}

So, (x+10)^{2 }+ (y+8)^{2}= 144

- Therefore , by comparing with the standard equation the coordinates of the center of the circle are

(h, k) = (−10, −8)

### Related Questions to study

Maths-

The graph of the linear function *f *is shown in the *xy*-plane above. The slope of the graph of the linear function *g *is 4 times the slope of the graph of *f*. If the graph of *g *passes through the point ( 0, −4), what is the value of *g*(9 ) ?

The graph of the linear function *f *is shown in the *xy*-plane above. The slope of the graph of the linear function *g *is 4 times the slope of the graph of *f*. If the graph of *g *passes through the point ( 0, −4), what is the value of *g*(9 ) ?

Maths-General

Maths-

### The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

### The mean score of 8 players in a basketball game was 14.5 points. If the highest individual score is removed, the mean score of the remaining 7 players becomes 12 points. What was the highest score?

Maths-General

Maths-

### If a^{2} + b^{2} = z and ab = y, which of the following is equivalent to 4z + 8y ?

### If a^{2} + b^{2} = z and ab = y, which of the following is equivalent to 4z + 8y ?

Maths-General

Maths-

### Intersecting lines r, s and t are shown below .

### Intersecting lines r, s and t are shown below .

Maths-General

Maths-

### The surface area of a cube is 6(a/4)^{2},where *a *is a positive constant. Which of the following gives the perimeter of one face of the cube?

### The surface area of a cube is 6(a/4)^{2},where *a *is a positive constant. Which of the following gives the perimeter of one face of the cube?

Maths-General

Maths-

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

If (x, y) is a solution of the system of equations above and x > 0, what is the value of xy ?

Maths-General

Maths-

In triangle *ABC *above, side AC is extended to

point *D*. What is the value of *y-x*?

**Note: **

It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

In triangle *ABC *above, side AC is extended to

point *D*. What is the value of *y-x*?

Maths-General

**Note: **

It is important to know the basic properties of a triangle to solve such problems. The most important property to remember is; the sum the interior angles of a triangle is 180°. This is often used in solving problems in geometry.

Maths-

### A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, *p *people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of *p *?

### A psychologist set up an experiment to study the tendency of a person to select the first item when presented with a series of items. In the experiment, 300 people were presented with a set of five pictures arranged in random order. Each person was asked to choose the most appealing picture. Of the first 150 participants, 36 chose the first picture in the set. Among the remaining 150 participants, *p *people chose the first picture in the set. If more than 20% of all participants chose the first picture in the set, which of the following inequalities best describes the possible values of *p *?

Maths-General

Maths-

### In air, the speed of sound *S*, in meters per second, is a linear function of the air temperature *T*, in degrees Celsius, and is given by *S(T) *= 0.6*T* + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

### In air, the speed of sound *S*, in meters per second, is a linear function of the air temperature *T*, in degrees Celsius, and is given by *S(T) *= 0.6*T* + 331.4. Which of the following statements is the best interpretation of the number 331.4 in this context?

Maths-General

Maths-

### Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of *x *and *y*, where *x *is the number of hours she tutors and *y *is the number of hours she works as a lifeguard?

### Jackie has two summer jobs. She works as a tutor, which pays $12 per hour, and she works as a lifeguard, which pays $9.50 per hour. She can work no more than 20 hours per week, but she wants to earn at least $220 per week. Which of the following systems of inequalities represents this situation in terms of *x *and *y*, where *x *is the number of hours she tutors and *y *is the number of hours she works as a lifeguard?

Maths-General

Maths-

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

Townsend Realty purchased the Glenview Street property and received a 40% discount off the original price along with an additional 20% off the discounted price for purchasing the property in cash. Which of the following best approximates the original price, in dollars, of the Glenview Street property?

Maths-General

Maths-

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The relationship between the monthly rental price *r*, in dollars, and the property’s purchase price *p*, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

The Townsend Realty Group invested in the five different properties listed in the table above. The table shows the amount, in dollars, the company paid for each property and the corresponding monthly rental price, in dollars, the company charges for the property at each of the five locations.

The relationship between the monthly rental price *r*, in dollars, and the property’s purchase price *p*, in thousands of dollars, can be represented by a linear function. Which of the following functions represents the relationship?

Maths-General

Maths-

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one

of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated

professional activity is research?

In a survey, 607 general surgeons and orthopedic surgeons indicated their major professional activity. The results are summarized in the table above. If one

of the surgeons is selected at random, which of the following is closest to the probability that the selected surgeon is an orthopedic surgeon whose indicated

professional activity is research?

Maths-General

Maths-

The system of equations above has solution *(x, y). *What is the value of *x *?

The system of equations above has solution *(x, y). *What is the value of *x *?

Maths-General

Maths-

### In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

### In State X, Mr. Camp’s eighth-grade class consisting of 26 students was surveyed and 34.6 percent of the students reported that they had at least two siblings. The average eighth‑grade class size in the state is 26. If the students in Mr. Camp’s class are representative of students in the state’s eighth-grade classes and there are 1,800 eighth-grade classes in the state, which of the following best estimates the number of eighth‑grade students in the state who have fewer than two siblings?

Maths-General