Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Mixed Review - Page 858: 55

See below

Rewrite the equation: $$x^2-y^2+14x+16y-5=0\\(x^2+14x)-(y^2-16y)-5=0\\(x^2+14x+49-49)-(y^2-16y+64-64)-5=0\\(x^2+14x+49)-(y^2-16y+64)=46+64+5\\(x+7)^2-(y-8)^2=-10\\\frac{(x+7)^2}{-10}-\frac{(y-8)^2}{-10}=0\\\frac{(y-8)^2}{10}-\frac{(x+7)^2}{10}=1$$ This is a standard form of a hyperbola.