Find the equations of tangent and normal lines at a point

$$(3, \frac{12}{5})$$

to ellipse

$$\frac{x^2}{25} + \frac{y^2}{9} = 1\text{.}$$

For what value of $c$ the line $x + y + c = 0$ will touch the ellipse

$$\frac{x^2}{25} + \frac{y^2}{9} = 1\text{?}$$