Find the Points at Which the Graph of the Equation $$5 x ^ { 2 } + 4 y ^ { 2 } - 10 x + 24 y + 8 = 0$$

Multiple Choice

Find the points at which the graph of the equation has a vertical or horizontal tangent line. $$5 x ^ { 2 } + 4 y ^ { 2 } - 10 x + 24 y + 8 = 0$$

A) There is a vertical tangent at $y = - 3$ but no horizontal tangents.
B) There is a horizontal tangent at $x = 1$ and a vertical tangent at $y = - 3$ .
C) There is a horizontal tangent at $x = 1$ but no vertical tangents.
D) There is a horizontal tangent at $x = - 2$ and a vertical tangent at $y = - 2$
E) There are no horizontal or vertical tangent lines.