1)Write an equation for an ellipse if the endpoints of the major axis are at(1,6)and (1,-6)and the endpoints of the minor axis are at (5,0)and (-3,0)
answer= (x-1)^2/36+y^2/16=1
2)Which is the equation of an ellipse with center (-4,2)and a horizontal major axis?
answer= (x-4)^2/16+(y-2)^2/4=1
3)Find the center and radius of the circle with equation x^2+(y-4)^2=9
answer= (0,4);3
4)Write the equation x^2-2x+y^2+4y=11 in standard form.
answer= (x-1)^2+(y+2)^2=16
5)Write the equation 4x^2+24x-y+34=0 in standard form
answer= y= 4(x-3)^2+2
#3 - correct
To find the center and radius of a circle given its equation, you can compare the equation to the standard form of a circle equation:
(x - h)^2 + (y - k)^2 = r^2
In this case, the equation is x^2 + (y - 4)^2 = 9.
Comparing it to the standard form, we can see that the center of the circle is (h, k) = (0, 4) (the opposite signs of the terms), and the radius is r = sqrt(9) = 3.
So, the center of the circle is (0, 4) and the radius is 3.