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?
1. Would (0,-7) work? ANS: Si
2,3 correct.
1) Yes, your intercepts for the graph of the equation y^2 = x + 49 are (-49, 0) and (0, 7). Good job!
2) Yes, you correctly wrote the standard form of the equation of the circle with radius 3 and center (-6, 9). The equation is (x + 6)^2 + (y - 9)^2 = 9.
3) Yes, you correctly found the center (h, k) as (7, 1) and the radius r as 9 for the circle with the equation (x - 7)^2 + (y - 1)^2 = 81. Well done!
1) For the first question, finding the intercepts of the graph of the equation y^2 = x + 49, you correctly plugged in 0 for x and obtained two intercept points. However, when you plugged in y = 0, you should have solved for x instead of y. Let's correct the calculation:
To find the x-intercepts, set y = 0 and solve for x:
0^2 = x + 49
x = -49
So, the x-intercept is (-49, 0).
To find the y-intercepts, set x = 0 and solve for y:
y^2 = 0 + 49
y^2 = 49
y = ±7
Thus, the y-intercepts are (0, -7) and (0, 7).
The correct intercepts for the equation y^2 = x + 49 are (-49, 0), (0, -7), and (0, 7).
2) Moving on to the second question, you were asked to write the standard form of the equation of a circle with radius 3 and center (-6, 9). Your answer, (x+6)^2 + (y-9)^2 = 9, is incorrect.
To write the equation of a circle in standard form, use the formula:
(x-h)^2 + (y-k)^2 = r^2
where (h, k) represents the center of the circle, and r represents the radius.
Using the given values, we have:
(x+6)^2 + (y-9)^2 = 3^2
(x+6)^2 + (y-9)^2 = 9
So, the correct standard form of the equation is (x+6)^2 + (y-9)^2 = 9.
3) Finally, for the third question, you were asked to find the center (h, k) and radius r of the circle with the equation (x-7)^2 + (y-1)^2 = 81.
Your answer of center = (7,1) and radius = 9 is incorrect.
Comparing the given equation to the standard form (x-h)^2 + (y-k)^2 = r^2, we can see that:
- The center (h, k) is (7, 1).
- The radius r is the square root of 81, which is 9.
Therefore, the correct center is (7, 1), and the correct radius is 9.
I hope this helps you verify your answers! Let me know if you have any more questions or if there's anything else I can assist you with.