Coordinate geometry is one of the highest-weightage units in JEE Mathematics. This set covers slopes and angles between lines, distances from a line, the equation of a circle and its tangents, and the standard parabola, ellipse and hyperbola, with a short solution for each question.
How to practise: read each question and tap the option you think is correct. You will see right away whether you got it, along with a short explanation, and your score is tracked at the bottom of the screen. This set has 15 questions.
Topics covered in this set
- Slope, angle between lines and perpendicular lines
- Distance of a point from a line and between parallel lines
- Centre, radius and diameter form of a circle
- Tangents and length of a tangent
- Parabola: focus, latus rectum and tangency
- Ellipse and hyperbola: eccentricity and foci
JEE Mathematics MCQs with answers and explanations
Q1. What is the slope of the line through (1, 2) and (4, 8)?
a) 6
b) 2
c) 3
d) 1/2
Q2. What is the perpendicular distance of the point (3, 4) from the line 3x + 4y − 5 = 0?
a) 20
b) 5
c) 4
d) 3
Q3. What is the acute angle between the lines y = x and y = √3 x?
a) 45°
b) 15°
c) 30°
d) 60°
Q4. Which line passes through (1, 1) and is perpendicular to 2x + 3y = 5?
a) 3x − 2y − 1 = 0
b) 2x + 3y − 5 = 0
c) 3x + 2y − 5 = 0
d) 2x − 3y + 1 = 0
Q5. What is the distance between the parallel lines 3x + 4y = 7 and 3x + 4y = 17?
a) 5
b) 1
c) 10
d) 2
Q6. What are the centre and radius of x² + y² − 4x + 6y − 12 = 0?
a) Centre (−2, 3), radius 5
b) Centre (2, −3), radius √12
c) Centre (2, −3), radius 5
d) Centre (4, −6), radius 5
Q7. What is the equation of the tangent to x² + y² = 25 at the point (3, 4)?
a) 3x + 4y = 25
b) 3x − 4y = 25
c) 4x + 3y = 25
d) 3x + 4y = 5
Q8. What is the length of the tangent from (5, 5) to the circle x² + y² = 9?
a) √50
b) √41
c) √59
d) 4
Q9. Which circle has the points (1, 2) and (5, 6) as the ends of a diameter?
a) x² + y² − 6x − 8y − 17 = 0
b) x² + y² − 3x − 4y + 17 = 0
c) x² + y² − 6x − 8y + 17 = 0
d) x² + y² + 6x + 8y + 17 = 0
Q10. What is the focus of the parabola y² = 12x?
a) (12, 0)
b) (3, 0)
c) (−3, 0)
d) (0, 3)
Q11. What is the length of the latus rectum of the parabola x² = −16y?
a) 16
b) −16
c) 4
d) 8
Q12. What is the eccentricity of the ellipse x²/25 + y²/16 = 1?
a) 3/4
b) 3/5
c) 4/5
d) 5/3
Q13. What is the distance between the foci of the ellipse x²/25 + y²/9 = 1?
a) 10
b) 8
c) 6
d) 4
Q14. What is the eccentricity of the hyperbola x²/16 − y²/9 = 1?
a) 3/4
b) 5/3
c) 4/5
d) 5/4
Q15. For what value of c is the line y = x + c a tangent to the parabola y² = 8x?
a) 4
b) 2
c) 8
d) 1
Quick revision notes
- Perpendicular slopes: m₁m₂ = −1; tan θ = |(m₁ − m₂)/(1 + m₁m₂)|.
- Distance of (x₁, y₁) from ax + by + c = 0 is |ax₁ + by₁ + c|/√(a² + b²).
- x² + y² + 2gx + 2fy + c = 0: centre (−g, −f), r = √(g² + f² − c).
- y² = 4ax: focus (a, 0), latus rectum 4a, tangent condition c = a/m.
- Ellipse b² = a²(1 − e²); hyperbola b² = a²(e² − 1); foci (±ae, 0).
Frequently asked questions
Are these JEE previous year questions?
No. They are original practice questions at the JEE Main level.
How do I tell an ellipse from a hyperbola in standard form?
In x²/a² + y²/b² = 1 both terms are positive (ellipse). In x²/a² − y²/b² = 1 one term is subtracted (hyperbola).
What is the fastest way to write a tangent at a given point?
Replace x² by xx₁, y² by yy₁, x by (x + x₁)/2 and y by (y + y₁)/2 in the equation of the curve. This works for circles and all standard conics.
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