$\"\"$

The function is $\"\\small$ and point on the curve is $\"(x_{0},$ .

Consider $\"\\small$ .

Apply derivative on each side with respect to $\"\\small$ .

$\"\\frac{d}{dx}f(x)=\\frac{d}{dx}\\left$

$\"f\'(x)$

Slope of the tangent line at point $\"(x_{0},$ is $\"f\'(x)=\\frac{y_{0}-y}{x_{0}-x}\"$ .

Substitute $\"(x_{0},$ in the slope of the tangent line.

$\"\\\\f\'(x)=\\frac{0-y}{5-x}$

$\"\"$

Slope of the tangent line is the derivative of the function.

Substitute $\"f\'(x)$ and $\"\\small$ in the slope of the tangent line.

$\"\\small$

$\"\\small$

Substitute $\"\\small$ in the function.

$\"\\small$

The point of tangency is $\"(x,$ .

Slope of the tangent line at $\"\\small$ is

$\"\\\\f\'(x)=\\frac{-2}{\\left$

Slope of the tangent line at $\"m=-\\frac{8}{25}\"$ .

$\"\"$

Point slope form of line equation is $\"(y-y_{1})=m(x-x_{1})\"$ .

Substitute $\"m=-\\frac{8}{25}\"$ and $\"(x,$ in the point-slope form.

$\"\\\\\\left$

Tangent line equation is $\"8x+25y-40=0\"$ .

$\"\"$

The point of tangency is $\"(x,$ .

Tangent line equation is $\"8x+25y-40=0\"$ .