Mathematics — Coordinate Geometry for the JEE Main Exam — Karnataka candidates

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.
• 6KEA (Karnataka Examinations Authority) issues a separate KCET admit card — KCET, JEE Main, and NEET have non-overlapping dates so a typical student sits all three.
• 7NEET-UG is offered in Kannada (ಕನ್ನಡ) at all KA centres. JEE Main and GATE are English/Hindi only — confirm your medium when applying.
• 8For GATE: Karnataka hosts 12+ test cities including Bengaluru, Mysuru, Mangaluru, and Hubballi; pick a centre near your university to avoid intercity travel on test day.

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).

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