1)Write an equation for the parabola with focus (1,3)and vertex(0,3)
answer= x= 1/4(y-3)^2
2)Write an equation for a circle if the endpoints of a diameter are at (1,1)and(1,-9)
answer= (x-1)^2+(y+4)^2=25
3)Which is the equation of a circle with center (0,1)and radius 2 units?
answer= x^2+y^2-2y=4
1) correct for the vertex but I don't know about the focus
2) wrong ( I again plugged your equation into my calculator and I didn't get the diameter as what was given)
3) correct
what do you mean?
for number 2
A.(x-1)^2+(y+4)^2=5
C.(x+1)^2+(y-4)^2=5
D.(x+1)^2+(y-4)^2=25
is it A?
number 1
A.y=(x-4)^2-15
B.y=4(x-1)^2+5
C.y=4(x-1)^2-3
Checking again..2 is fine
I was looking on the wrong side of the circle for the diameter points.
I apologize for the confusion earlier. Let's re-evaluate the answers:
1) The equation for a parabola with focus (1,3) and vertex (0,3) can be found using the formula (x-h)^2 = 4p(y-k), where (h,k) is the vertex and p is the distance between the focus and the vertex. In this case, the vertex is (0,3) and the focus is (1,3). The distance between the vertex and focus is 1 unit, so p = 1. Plugging in the values, we get:
(x-0)^2 = 4(1)(y-3)
x^2 = 4(y-3)
x^2 = 4y - 12
The correct answer for this one is B.
2) The equation for a circle with endpoints of a diameter at (1,1) and (1,-9) can be found using the formula (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In this case, the two endpoints lie on a vertical line, so the x-coordinate of the center will be the same as the x-coordinate of the endpoints (1 in this case). The y-coordinate of the center can be found by taking the average of the y-coordinates of the endpoints: (1+(-9))/2 = -4.
Plugging in the values, we get:
(x-1)^2 + (y+4)^2 = r^2
(r^2 is the square of the radius, which we need to find)
Now, we can use one of the endpoints to find the radius. Let's use (1,1):
(1-1)^2 + (1+4)^2 = r^2
5^2 = r^2
25 = r^2
Therefore, the correct equation is (x-1)^2 + (y+4)^2 = 25. The correct answer for this one is D.
3) The equation of a circle with center (0,1) and radius 2 units can be found using the formula (x-a)^2 + (y-b)^2 = r^2, where (a,b) is the center of the circle and r is the radius. In this case, the center is (0,1) and the radius is 2 units.
Plugging in the values, we get:
(x-0)^2 + (y-1)^2 = 2^2
x^2 + (y-1)^2 = 4
x^2 + y^2 - 2y + 1 = 4
x^2 + y^2 - 2y - 3 = 0
Therefore, the correct equation is x^2 + y^2 - 2y - 3 = 0. The correct answer for this one is D.