Cartesian Equation of Parabola

The video tutorial explores the concept of conic sections, focusing on parabolas. It explains how the intersection of a plane with a double napped cone forms different shapes, including parabolas. The tutorial highlights the practical applications of parabolic shapes in everyday life, such as in fountains, headlights, and bridges. It defines a parabola as the locus of a point equidistant from a fixed point and a line, and introduces associated terms like focus, directrix, and vertex. The video also discusses the equations of parabolas and their symmetry properties.

What shape is formed when a plane cuts a double napped cone at an angle equal to the vertical angle of the cone?

• Ellipse

• Hyperbola

• Circle

• Parabola

Which of the following is an example of a parabolic shape in everyday life?

• A TV dish antenna

• A rectangular table

• A square window

• A circular plate

What is the eccentricity of a parabola?

• Greater than 1

• Less than 1

• 0

• 1

What is the degenerate case of a parabola when the fixed point lies on the fixed line?

• A straight line

• A circle

• An ellipse

• A hyperbola

What is the fixed point of a parabola called?

• Directrix

• Axis

• Focus

• Vertex

Which term describes a chord that passes through the focus of a parabola?

• Directrix

• Focal chord

• Axis

• Vertex

What is the equation of a parabola with its vertex at the origin and focus at (a, 0)?

• x^2 = 4ay

• y^2 = 4ax

• x^2 = 4ax

• y^2 = 4ay

What is the length of the latus rectum of a parabola with equation y^2 = 4ax?

• 4a

• 5a

• 3a

• 2a

A parabola is symmetric about which line if its equation contains a y^2 term?

• Line y = x

• X-axis

• Y-axis

• Line y = -x

If a parabola's equation contains an x^2 term, about which axis is it symmetric?

• Line y = x

• Line y = -x

• Y-axis

• X-axis