Question

Identify the type of conic section that has the equation 9x2+ 16y2 = 144 and identify its domain and range.

ellipse
Domain: {–3 ≤ x ≤ 3}
Range: {–4 ≤ y ≤ 4}

ellipse
Domain: {–4 ≤ x ≤ 4}
Range: {–3 ≤ y ≤ 3}

hyperbola
Domain: all real numbers
Range: {y ≤ –4 or y ≥ 4}

hyperbola
Domain: {x ≤ –4 or x ≥ 4}
Range: all real numbers

Answer 1

9 x² + 16 y² = 144 / : 144 ( divide both sides by 144 )
x²/16 + y²/ 9 = 1 ( ellipse )
a² = 16, a = 4
b² = 9, b = 3
Answer:
B ) ellipse;
Domain : { -4 ≤ x ≤4 }
Range: { -3 ≤ y ≤ 3 }