Conic Sections — MHT-CET Maths

Formulas (2)

• Standard Forms, Focus, Directrix and Latus Rectum · Parabola y² = 4ax
  $$y^2 = 4ax: \quad S(a, 0), \quad x = -a, \quad LR = 4a$$
• Tangents: y = mx + a/m, Pairs of Tangents and Angles Between Curves · Tangency condition
  $$y = mx + c \text{ touches } y^2 = 4ax \iff c = \frac{a}{m}$$

Watch out for (6)

• Putting the directrix on the same side as the focus
  → Standard Forms, Focus, Directrix and Latus Rectum
• Reading 4a as a
  → Standard Forms, Focus, Directrix and Latus Rectum
• Forgetting the sign when completing the square
  → Standard Forms, Focus, Directrix and Latus Rectum
• Using c = a/m for an upward parabola
  → Tangents: y = mx + a/m, Pairs of Tangents and Angles Between Curves
• Forgetting the modulus in the angle
  → Tangents: y = mx + a/m, Pairs of Tangents and Angles Between Curves
• Differentiating the wrong variable
  → Tangents: y = mx + a/m, Pairs of Tangents and Angles Between Curves

Formulas (2)

• Eccentricity and Foci of the Ellipse and Hyperbola · Eccentricity
  $$\text{ellipse: } b^2 = a^2(1 - e^2) \qquad \text{hyperbola: } b^2 = a^2(e^2 - 1)$$
• Tangents of a Given Slope, and Curves That Cut at Right Angles · Tangent of slope m
  $$\text{ellipse: } c^2 = a^2m^2 + b^2 \qquad \text{hyperbola: } c^2 = a^2m^2 - b^2$$

Watch out for (6)

• Dividing by the wrong denominator
  → Eccentricity and Foci of the Ellipse and Hyperbola
• Using the ellipse relation for a hyperbola
  → Eccentricity and Foci of the Ellipse and Hyperbola
• Forgetting the 2 in the parametric form
  → Eccentricity and Foci of the Ellipse and Hyperbola
• Using the ellipse sign for a hyperbola
  → Tangents of a Given Slope, and Curves That Cut at Right Angles
• Not writing the ellipse in standard form first
  → Tangents of a Given Slope, and Curves That Cut at Right Angles
• Slope of a perpendicular line
  → Tangents of a Given Slope, and Curves That Cut at Right Angles