The discriminant of the quadratic equation is negative, indicating imaginary lines.

Rearranging gives (x-2)^2 + (y-2)^2 = 0, which represents two intersecting lines.

To determine the nature of the lines, we can rewrite the equation in the form of (x - a)^2 + (y - b)^2 = r^2 and analyze the discriminant.

Rearranging gives (x-2)^2 + (y-3)^2 = 0, which represents a single point, hence the lines are coincident.

To determine the nature of the lines, we can find the slopes from the equation. The product of the slopes will help us conclude if they are perpendicular.

The given equation can be factored as (x - 2y)(x - 2y) = 0, indicating that the lines are perpendicular.

Since the coefficient of (x - 2)^2 is negative, the parabola opens downwards.

The stigma is the part of the pistil that receives pollen during fertilization.

The Parthenon is dedicated to Athena, the goddess of wisdom and warfare, and is a quintessential example of ancient Greek architecture.

The phenomenon of a liquid rising in a narrow tube is called capillarity.

Diffraction is the bending of light waves around obstacles and openings.

Diffraction is the bending of light waves around obstacles and openings.

Capillary action occurs due to the combination of surface tension (which pulls the liquid up) and adhesion (which attracts the liquid to the walls of the tube).

Electromagnetic induction was discovered by Michael Faraday.

The phenomenon of liquid rising in a narrow tube is called capillarity.

Surface tension arises from cohesive forces between liquid molecules.

Utilitarianism is most closely associated with John Stuart Mill, who expanded on Jeremy Bentham's ideas about maximizing happiness.

The 'Allegory of the Cave' is found in 'The Republic', illustrating the difference between the world of appearances and the world of reality.

'Tabula Rasa' is the theory that individuals are born as blank slates, with knowledge and personality shaped by experience.

A 'double-edged sword' implies that something has both positive and negative consequences, which aligns with the discussion in the passage.

A 'double-edged sword' implies that something can have both beneficial and harmful consequences.

'In the wake of' refers to events that occur as a result of something else, typically after it.

'Inextricably linked' means that two concepts are so closely connected that they cannot be separated, which is the intended meaning in the passage.

The phrase implies the necessity of staying current with technological advancements, thus option 1 is correct.

To 'take with a grain of salt' means to view something with skepticism or not to take it literally.

Liberalism played a crucial role in the planning and execution of the French Revolution, advocating for individual rights and democratic governance.

The Indus Valley Civilization is known for its advanced urban planning, including complex irrigation systems that supported agriculture.

The Roman Empire's extensive road network was primarily designed to facilitate military mobilization, allowing for quick movement of troops across the empire.

The Maurya Empire implemented policies to increase agricultural productivity, which in turn supported a larger labor force and population growth.

The potential energy U of a system of two point charges is given by U = k * q1 * q2 / r.