Find the Equation of the Circle That Satisfies the Following

question 19

Multiple Choice

Find the equation of the circle that satisfies the following conditions. Express the final equation in the form x ² + y ² + Dx + Ey + F = 0. Tangent to the x axis, a radius of length 2, and abscissa of center is -1

• A) x ² + y ² - 2 x - 4 y + 1 = 0 and x ² + y ² - 2 x + 4 y + 1 = 0
• B) x ² + y ² + 2 x - 4 y + 1 = 0
• C) x ² + y ² + 2 x - 4 y + 1 = 0 and x ² + y ² + 2 x + 4 y + 1 = 0
• D) x ² + y ² + 2 x + 4 y + 1 = 0
• E) x ² + y ² - 2 x + 4 y + 1 = 0

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Definitions:

Triplet

In chemistry and physics, refers to a quantum state with three possible orientations in a magnetic or spin system.

Broad Singlet

A term in nuclear magnetic resonance (NMR) spectroscopy describing a signal that appears as a single peak but with a broadened width due to various intermolecular interactions.

NMR Data

Information obtained from nuclear magnetic resonance spectroscopy, used to determine molecular structure and dynamics.

Quartet

A pattern of four peaks observed in nuclear magnetic resonance (NMR) spectroscopy, typically arising from a hydrogen atom coupled with three equivalent hydrogens.