Maths-
General
Easy
Question
The graph of x2 - 4x + y2 + 6y - 24 = 0 in the xy- plane is a circle. What is the radius of the circle ?
The correct answer is:
HINT: Use completing the square method and find the radius of the circle.
Complete step by step solution:
Given equation is x2 - 4x + y2 + 6y - 24 = 0
On adding 24 on both the sides, we get x2 - 4x + y2 + 6y = 24
Lets apply the completing square method, i. e take half of the coefficient of x term and y term from the given equation
and square it. Then add it to the equation.
The coefficient of x- term is -4 and its half is -2. The square of -2 is 4.
Likewise, the coefficient of y-term is 6 and half of it is 3. The square of 3 is 9.
Let’s add these numbers, 4 and 9 on both LHS and RHS to balance the given equation.
Now, we get x2 - 4x + 4 + y2 + 6y + 9 = 24 + 4 + 9
x2 - 4x + 4 + y2 + 6y + 9 = 24 + 4 + 9 can be written as (x - 2)2 + (y + 3)2 = 37
[Since x2 - 4x + 4 = (x - 2)2 and y2 + 6y + 9 = (y + 3)2]
We know that the circle’s equation is (x - h)2 + (y - k)2 = r2 where, r is the radius, h and k are x and y
coordinates of the center of the circle respectively.
However, on comparing the Circle’s equation with the simplified equation, it is evident that r2 = 37
So, r =
Hence option C is the answer.
Related Questions to study
Maths-
The boiling point of water at sea level is 212 degrees Fahrenheit ( ∘F). For every increase of 1,000 feet above sea level, the boiling point of water drops approximately 1.84∘ F. Which of the following equations gives the approximate boiling point B, in ∘F, at h feet above sea level?
The boiling point of water at sea level is 212 degrees Fahrenheit ( ∘F). For every increase of 1,000 feet above sea level, the boiling point of water drops approximately 1.84∘ F. Which of the following equations gives the approximate boiling point B, in ∘F, at h feet above sea level?
Maths-General
Maths-
The number of people who go to a public swimming pool can be modeled by the function g above, where c is a constant and t is the air temperature in degrees Fahrenheit ( ∘F) for 70 < t < 100. If 350 people are predicted to go to the pool when the temperature is 90∘ F, what is the value of c ?
The number of people who go to a public swimming pool can be modeled by the function g above, where c is a constant and t is the air temperature in degrees Fahrenheit ( ∘F) for 70 < t < 100. If 350 people are predicted to go to the pool when the temperature is 90∘ F, what is the value of c ?
Maths-General
Maths-
Which of the following is an equivalent form of 
, where f > 0 and k > 0 ?
Which of the following is an equivalent form of , where f > 0 and k > 0 ?
Maths-General
Maths-
For a positive real number x, where x8 = 2, what is the value of x24 ?
For a positive real number x, where x8 = 2, what is the value of x24 ?
Maths-General
Maths-
Which of the following expressions is equivalent to the one above, where x ≠ 1 ?
Which of the following expressions is equivalent to the one above, where x ≠ 1 ?
Maths-General
Maths-
x2 - 6x + 11 = y
x = y + 1
The system of equations above is graphed in the xy-plane. Which of the following is the y-coordinate of an intersection point (x, y) of the graphs of the two equations?
x2 - 6x + 11 = y
x = y + 1
The system of equations above is graphed in the xy-plane. Which of the following is the y-coordinate of an intersection point (x, y) of the graphs of the two equations?
Maths-General
Maths-
x + 2y = 16
0.5x - y = 10
The solution to the system of equations above is (x, y). What is the value of x ?
x + 2y = 16
0.5x - y = 10
The solution to the system of equations above is (x, y). What is the value of x ?
Maths-General
Maths-
0.8p = t
At a store, a coat originally priced at p dollars is on sale for t dollars, and the relationship between p and t is given in the equation above. What is p in terms of t ?
0.8p = t
At a store, a coat originally priced at p dollars is on sale for t dollars, and the relationship between p and t is given in the equation above. What is p in terms of t ?
Maths-General
Maths-
In the figure above, 
and 
are parallel, 
and 
are parallel, CD = CE, and the measure of 
is 1150. What is the measure of 
?
In the figure above, and are parallel, and are parallel, CD = CE, and the measure of is 1150. What is the measure of ?
Maths-General
Maths-
x(x + 2) = 8
Which of the following lists all solutions to the quadratic equation above?
x(x + 2) = 8
Which of the following lists all solutions to the quadratic equation above?
Maths-General
Maths-
5x2 - 3(1 - x) - 2x(x + 5)
Which of the following polynomials is equivalent to the expression above?
5x2 - 3(1 - x) - 2x(x + 5)
Which of the following polynomials is equivalent to the expression above?
Maths-General
Maths-
C = 10x + 4y
The formula above gives the monthly cost C, in dollars, of operating a delivery truck when the driver works a total of x hours and when y gallons of gasoline are used. If, in a particular month, it cost no more than $ 2,000 to operate the truck and at least 150 gallons of gas were used, what is the maximum number of hours the driver could have worked?
C = 10x + 4y
The formula above gives the monthly cost C, in dollars, of operating a delivery truck when the driver works a total of x hours and when y gallons of gasoline are used. If, in a particular month, it cost no more than $ 2,000 to operate the truck and at least 150 gallons of gas were used, what is the maximum number of hours the driver could have worked?
Maths-General
Maths-
A farmer sold 108 pounds of produce that consisted of z pounds of zucchini and c pounds of cucumbers. The farmer sold the zucchini for $ 1.69 per pound and the cucumbers for $ 0.99 per pound and collected a total of $ 150.32. Which of the following systems of equations can be used to find the number of pounds of zucchini that were sold?
A farmer sold 108 pounds of produce that consisted of z pounds of zucchini and c pounds of cucumbers. The farmer sold the zucchini for $ 1.69 per pound and the cucumbers for $ 0.99 per pound and collected a total of $ 150.32. Which of the following systems of equations can be used to find the number of pounds of zucchini that were sold?
Maths-General
English-One-to-One
The idiom ‘A change of heart’ means_______.
The idiom ‘A change of heart’ means_______.
English-One-to-OneGeneral
General
Choose the one which best expresses the meaning of the idioms and phrases: Ram sold their house because it was a real white elephant
Choose the one which best expresses the meaning of the idioms and phrases: Ram sold their house because it was a real white elephant
GeneralGeneral
