These questions that I have completed are on a test review for my exam and I would just like to know if they are correct. These are only a few of the questions, I have more that are just not complete yet. Thank You!
1) List the intercepts for the graph of the following equation.
y^2 = x + 49
I plugged in 0 for x and then y and I got (-49,0) and (0,7).
2) Write the standard form of the equation of the circle with radius and center (h,k)
r=3 (h,k)=(-6,9)
(x+6)^2 + (y-9)^2 = 9
3) Find the center (h,k) and radius r of the circle with the given equation.
(x-7)^2 + (y-1)^2 = 81
center = (7,1) radius =9
Are these correct?
Based on the information provided, your answers for questions 1, 2, and 3 are correct.
1) To find the intercepts of the equation y^2 = x + 49, you correctly plugged in 0 for x and y and obtained (-49, 0) and (0, 7). These points represent the x-intercept and the y-intercept of the graph, respectively.
2) The standard form of the equation of a circle with radius r and center (h, k) is (x-h)^2 + (y-k)^2 = r^2. In this case, the radius is 3 and the center is given as (-6, 9). You correctly substituted these values into the standard form equation to obtain (x+6)^2 + (y-9)^2 = 9.
3) The equation (x-7)^2 + (y-1)^2 = 81 represents a circle. By comparing this equation to the standard form of a circle equation, you can identify that the center is (h, k) = (7, 1) and the radius is given by r^2 = 81, so r = 9. Therefore, your answer of center = (7,1) and radius = 9 is correct.
Remember, it's always a good idea to double-check your work and make sure you followed the correct steps in solving these types of questions.