Write an equation for the translation of circle x^2+y^2=25, 2 units right and 4 units down.
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what is a bird
2-2
To translate a circle, we need to adjust the center of the circle by moving it horizontally and vertically. In this case, we are moving the circle 2 units to the right (along the x-axis) and 4 units down (along the y-axis).
The equation of a circle with center (h, k) and radius r is given by (x - h)^2 + (y - k)^2 = r^2.
Given the original circle equation x^2 + y^2 = 25, we need to translate it 2 units to the right and 4 units down.
To translate it 2 units to the right, we need to subtract 2 from the x-coordinate of the center, so the new x-coordinate of the center is 0 - 2 = -2.
To translate it 4 units down, we need to subtract 4 from the y-coordinate of the center, so the new y-coordinate of the center is 0 - 4 = -4.
So, the translated circle equation is:
(x - (-2))^2 + (y - (-4))^2 = 25
Simplifying:
(x + 2)^2 + (y + 4)^2 = 25
Therefore, the equation for the translated circle is (x + 2)^2 + (y + 4)^2 = 25.
Regarding your additional question, "What is a bird?", a bird is a warm-blooded, vertebrate animal characterized by feathers, beaked jaws, and the ability to fly. Birds belong to the class Aves in the animal kingdom and are found in various habitats around the world. They come in a wide range of sizes, shapes, and colors and have diverse adaptations for different types of environments and lifestyles.