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

Answer: B ) ellipse.

Domain: { -4 ≤ x ≤ 4 }

Range: { -3 ≤ y ≤ 3 }

Explanation:

Answer 2

9 x² + 16 y² = 144 /:144

`( x^(2) )/(16) + ( y^(2) )/(9) =1`
General formula of ellipse ( the center is at the origin ):
`( x^(2) )/( a^(2) )+ ( y^(2) )/( b^(2) ) =1`
a² = 16, b² = 9
Domain: [-a, a ] = [-4, 4]
Range:[-b, b ]
Answer: B ) ellipse.
Domain: { -4 ≤ x ≤ 4 }
Range: { -3 ≤ y ≤ 3 }