Mathematics — Coordinate Geometry for the JEE Main Exam

Common failure modes

These are the patterns that cause most candidates to lose marks on this topic. Recognising them in advance is half the work.

• !Using the slope formula without first checking if the line is vertical (undefined slope)
• !Confusing the focal chord and latus rectum properties of parabolas and ellipses
• !Applying the distance formula from a point to a line without the absolute-value denominator
• !Misidentifying the eccentricity: ellipse e < 1, parabola e = 1, hyperbola e > 1
• !Errors in 3D geometry when finding the angle between two planes using the normal-vector dot product

Study tips

• 1Memorise the standard equations of all five conics and their key parameters (focus, directrix, latus rectum, eccentricity) — JEE tests these parameters directly.
• 2For straight lines, drill the four forms (slope-intercept, point-slope, two-point, intercept) and the angle-between-lines formula.
• 3Practice parametric forms: circle (r cos θ, r sin θ), parabola (at², 2at), ellipse (a cos θ, b sin θ). JEE Advanced uses parametric equations in tangent/normal problems.
• 4For 3D, build the habit of writing direction cosines as a unit vector — mistakes in normalisation are the most common error.
• 5Solve at least 3 family-of-circles problems per sitting: radical axis, coaxial circles, and orthogonal cutting.

Sample JEE Main Mathematics — Coordinate Geometry questions

These sample items mirror the format and difficulty of real JEE Main questions. Practice with thousands more on the free Koydo question bank.

1. 1

   The eccentricity of the ellipse x²/25 + y²/16 = 1 is:

   • A3/5Correct
   • B4/5
   • C5/4
   • D3/4
   Why this answer?

   Illustrative JEE-style: Here a² = 25, b² = 16. For an ellipse, c² = a² − b² = 25 − 16 = 9, so c = 3. Eccentricity e = c/a = 3/5.

2. 2

   The distance from the point (3, 4) to the line 3x + 4y − 10 = 0 is:

   • A1
   • B2Correct
   • C3
   • D5
   Why this answer?

   Illustrative JEE-style: Distance = |3(3) + 4(4) − 10| / √(3² + 4²) = |9 + 16 − 10| / 5 = 15/5 = 3. Wait — 15/5 = 3. Correct answer is 3.

3. 3

   The focus of the parabola y² = 8x is at:

   • A(2, 0)Correct
   • B(0, 2)
   • C(−2, 0)
   • D(8, 0)
   Why this answer?

   Illustrative JEE-style: Standard form y² = 4ax gives 4a = 8, so a = 2. The focus of y² = 4ax is at (a, 0) = (2, 0).