Question 1 Consider the sphere $x^2 + y^2 + z^2 + 6x - 8y + 10z + 25 = 0$. 1. Find the radius of the sphere. r = 5 2. Find the distance from the center of the sphere to the plane $z = 1$. distance = 6 3. Find the distance from the center of the sphere to the y-axis. distance = 4 (enter sqrt(a) for $\sqrt{a}$; for example, enter 2sqrt(3) for $2\sqrt{3}$; must simplify your answers; do not insert a space or a multiplication operator)
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To find the radius of the sphere, we can rewrite the equation in the standard form of a sphere: (x - h)^2 + (y - k)^2 + (z - l)^2 = r^2, where (h, k, l) is the center of the sphere and r is the radius. In this case, we have x^2 + y^2 + z^2 + 6x + 8y + 10z + 25 = Show more…
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