Chapter 13, Trigonometric Ratios and Functions - 13.1 Use Trigonometry with Right Triangles - 13.1 Exercises - Mixed Review - Page 858: 53

$\dfrac{(x+9)^2}{100}+\dfrac{(y+5)^2}{36}=1$ ; Ellipse

Given: $9x^2+25y^2+162x+250y+454=0$ $[9x^2+(2)(27)(3x)+729]+25(y^2+5y+25)=729+625-454$ This gives: $(3x+27)^2+25(y+5)^2=(30)^2$ Thus, we have $\dfrac{(x+9)^2}{100}+\dfrac{(y+5)^2}{36}=1$ This is the standard form of an Ellipse.