Question

Identify the conic section from its equation,
(x-5)²/4 + (y+3)²/16 = 1

Answer 1

The conic section represented by the equation
`(x-5)^2/4 + (y+3)^2/16 = 1` ter at the point (5, -3).

Step-by-step explanation:

To identify the conic section from its equation
`(x-5)^2/4 + (y+3)^2/16 = 1` standard forms of conic section equations. This equation is in the form
`(x-h)^2/a^2 + (y-k)^2/b^2 = 1,` the conic, and a and b are the lengths of the semi-major axis and semi-minor axis, respectively. The presence of plus signs and a constant 1 on the right-hand side indicates that this is an equation of an ellipse.

The given equation, with its denominators being different positive numbers and the absence of a minus sign, fits the standard form of an ellipse's equation exactly. Therefore, the conic section represented by the equation
`(x-5)^2/4 + (y+3)^2/16 = 1` h its center at (5, -3).