STEM 307- Pre - Calculus (Midterms) Questions And Answers
Conic Sections - ANS-✔✔'conics', means taking cross sections of a cone, is formed when a plane
intercepts a double - napped right circular cone
Generator - ANS-✔✔A line on the cone
Vertex - ANS-✔✔only point where the generators meet
Vertical Axis - ANS-✔✔vertical line passing through the vertex
Directix - ANS-✔✔perimeter of the base of the cone
Nappe - ANS-✔✔lateral surface of a cone
Vertical Angle - ANS-✔✔angle between the generator and the vertical axis
4 Ways a Plane can Intersect a Cone - ANS-✔✔circle, ellipse, parabola, hyperbola
Degenerate Conics - ANS-✔✔conics where both the plane and the double right circular cone intersects
but fails to form a curve
Circle - ANS-✔✔set of all points P(x,y) in a plane whose distance from a fixed point called the center
(h,k) is a constant called the radius (r)
Characteristics of a Circle - ANS-✔✔~ quadratic in x and y
~ same coefficient
, Standard Forms of the Equation of a Circle - ANS-✔✔circle with center at (0,0): x² + y² = r²
circle with center at (h,k): (x - h)² + (y - k)² = r²
General Forms of the Equation of a Circle - ANS-✔✔circle with center at (0,0): x² + y² - r²= 0
circle with center at (h,k): x² + y² +Cx + Dy + E = 0
Solving for: Radius - ANS-✔✔r = √(x₂ - x₁)² + (y₂ - y₁)²
Solving for: Slope - ANS-✔✔m = y₂ - y₁ / x₂ - x₁
General Form of the Equation of a Line - ANS-✔✔Ax + By + C = 0
Point Slope Form Equation of a Line - ANS-✔✔y - y₁ = m(x₂ - x₁)
Two Point Form Equation of a Line - ANS-✔✔y - y₁ = (y₂ - y₁ / x₂ - x₁)(x₂ - x₁)
Slope Intercept Form Equation of a Line - ANS-✔✔y = mx + b
Intercept Form Equation of a Line - ANS-✔✔x/a + y/b = 1
Parabola - ANS-✔✔a locus of points whose distance from a fixed point(focus) is equal to the distance of
a fixed line(directix)
Latus Rectum (4p) - ANS-✔✔line connecting two points on the parabola and passing through foci
Conic Sections - ANS-✔✔'conics', means taking cross sections of a cone, is formed when a plane
intercepts a double - napped right circular cone
Generator - ANS-✔✔A line on the cone
Vertex - ANS-✔✔only point where the generators meet
Vertical Axis - ANS-✔✔vertical line passing through the vertex
Directix - ANS-✔✔perimeter of the base of the cone
Nappe - ANS-✔✔lateral surface of a cone
Vertical Angle - ANS-✔✔angle between the generator and the vertical axis
4 Ways a Plane can Intersect a Cone - ANS-✔✔circle, ellipse, parabola, hyperbola
Degenerate Conics - ANS-✔✔conics where both the plane and the double right circular cone intersects
but fails to form a curve
Circle - ANS-✔✔set of all points P(x,y) in a plane whose distance from a fixed point called the center
(h,k) is a constant called the radius (r)
Characteristics of a Circle - ANS-✔✔~ quadratic in x and y
~ same coefficient
, Standard Forms of the Equation of a Circle - ANS-✔✔circle with center at (0,0): x² + y² = r²
circle with center at (h,k): (x - h)² + (y - k)² = r²
General Forms of the Equation of a Circle - ANS-✔✔circle with center at (0,0): x² + y² - r²= 0
circle with center at (h,k): x² + y² +Cx + Dy + E = 0
Solving for: Radius - ANS-✔✔r = √(x₂ - x₁)² + (y₂ - y₁)²
Solving for: Slope - ANS-✔✔m = y₂ - y₁ / x₂ - x₁
General Form of the Equation of a Line - ANS-✔✔Ax + By + C = 0
Point Slope Form Equation of a Line - ANS-✔✔y - y₁ = m(x₂ - x₁)
Two Point Form Equation of a Line - ANS-✔✔y - y₁ = (y₂ - y₁ / x₂ - x₁)(x₂ - x₁)
Slope Intercept Form Equation of a Line - ANS-✔✔y = mx + b
Intercept Form Equation of a Line - ANS-✔✔x/a + y/b = 1
Parabola - ANS-✔✔a locus of points whose distance from a fixed point(focus) is equal to the distance of
a fixed line(directix)
Latus Rectum (4p) - ANS-✔✔line connecting two points on the parabola and passing through foci
