Find equation of circle with center (0,0) radius 5. 2) State equation of tangent to x2 + y2 = 25 at (3,4).

The equation of a circle with center $(h,k)$ and radius $r$ is given by:

Given center $(h,k) = (0,0)$ and radius $r = 5$.
Substitute $h=0$, $k=0$, and $r=5$ into the equation:

The equation of the circle is $\boxed{x^2 + y^2 = 25}$.

2) State equation of tangent to $x^2 + y^2 = 25$ at $(3,4)$

The given equation of the circle is $x^2 + y^2 = 25$.
This is a circle centered at the origin $(0,0)$ with $r^2 = 25$.

For a circle $x^2 + y^2 = r^2$, the equation of the tangent at a point $(x_1, y_1)$ on the circle is given by:

The point of tangency is $(x_1, y_1) = (3,4)$ and $r^2 = 25$.
Substitute $x_1=3$, $y_1=4$, and $r^2=25$ into the tangent equation:

The equation of the tangent is $\boxed{3x + 4y = 25}$.