VITEEE Maths Analytical Geometry Previous Year Questions

VITEEE Maths Analytical Geometry PYQ, free to download as a 25-page PDF. The bank carries 19 solved questions from the 2021 to 2025 papers and takes roughly one day to work through, so treat it as a single focused sitting.

Questions run newest year first, with the options exactly as printed. The answer key follows, then a worked solution for each one.

VITEEE Analytical Geometry Weightage

Mathematics is 40 of the 125 questions in VITEEE, the largest section in the paper. Unit 3 covers coordinate geometry, straight lines and conics, and it turned up in every year we looked at.

2022 was an outlier at eight questions. Papers up to 2025 awarded one mark with no penalty; from 2026 the scheme is plus four and minus one.

Formulas Worth Memorising

• Circle from the general form: centre is minus g, minus f, and the radius is the root of g squared plus f squared minus c
• Parabola y squared = 4ax: focus at a, 0, directrix x = minus a, latus rectum 4a
• Ellipse: e = root of 1 minus b squared over a squared
• Hyperbola: b squared = a squared times e squared minus 1, with the bracket the other way round
• Perpendicular lines have slopes whose product is minus one
• Distance from a point to a line: mod of a x plus b y plus c, over root a squared plus b squared

How to Approach the Set

Two points on an ellipse look like a hard simultaneous system until you substitute the reciprocals of a squared and b squared. Then it is a pair of linear equations and it falls out in three lines. The same trick appears twice in this bank.

For anything given as a general second-degree equation, complete the square first and read the standard form off. Do not try to shortcut to the eccentricity: which denominator is larger decides whether the major axis is horizontal or vertical, and that is only visible once it is in standard form.

Tangency questions all reduce to the same thing. Substitute, get a quadratic, and set the discriminant to zero.

Common Mistakes

• Reading the right-hand side of a circle equation as the radius rather than its square
• Putting the directrix on the same side of the vertex as the focus
• Assuming the major axis is horizontal without checking the denominators
• Using the ellipse eccentricity relation on a hyperbola
• Answering with the angle to the x-axis when the question asked about the y-axis

Two to Solve First

The 2025 question about the smallest circle touching two others looks intimidating and is not. Its diameter runs between the two nearest points, and because both given circles happen to have radius two, the centre is simply the midpoint of their centres.

Then the 2022 general conic. Completing the square turns it into a standard ellipse, and the larger denominator lands under y, so the major axis is vertical. Anyone who assumed horizontal gets a different eccentricity, and it is on the list.

Video Solutions

Source: Vedantu JEE Made Ejee

Using the Answer Key

Attempt all 19 before checking anything, allowing about ninety seconds each. Mark the key in one pass, right or wrong only, then read the solution for every miss and every lucky guess. Each opens with a one-line quick solution you can stop at and retry from.