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🚀 COMPLETE PREPARATION LOOP: LEARN → PRACTICE → ANALYZE

Coordinate Geometry Preparation Hub

Master Coordinate Geometry with coaching-grade theory notes, verified video lectures, and 10 interactive MCQs with instant mistake analysis. Continue with 500+ adaptive questions inside the Exam Sprinter app.

📘 Theory Notes ✍️ Interactive Practice ⏱️ CBT Simulator

What is Coordinate Geometry?

Coordinate Geometry covers the essential principles and concepts required for JEE Main.

💡 Why Study Coordinate Geometry?

Highly important, frequently tested in JEE Main.

Parameter	Details / Relevance
Target Exam	JEE Main
Subject Category	Mathematics
Estimated Study Duration	10 Hours
Expected Questions	2 Questions
Difficulty Index	Hard
Interactive Solved MCQs	10 Questions with AI Diagnostics
Adaptive App Practice	500+ Questions & Real-Time AI Tutor

⚠️ Common Pitfalls to Avoid

Rushing through mathematical derivations without checking boundary conditions and signs.
Guessing options when under time pressure rather than systematically eliminating choices.
Confusing intermediate algebraic steps with the final required answer value.

✓ COACHING-GRADE CLASSROOM NOTES

Coordinate Geometry Theory & Derivations

Browse All Notes Library ›

Access comprehensive classroom-grade derivations and NCERT micro-extracts for Coordinate Geometry. Features step-by-step proofs and standard assumptions.

Important Formulas & Cheat Sheet

Distance: $$d = \sqrt{(x_2-x_1)^2+(y_2-y_1)^2}$$
Circle: $$(x-h)^2+(y-k)^2=r^2$$
Ellipse: $$\frac{x^2}{a^2}+\frac{y^2}{b^2}=1$$

✍️ STEP 3: PRACTICE & ANALYZE

Coordinate Geometry Interactive Practice

⏱️ Take Chapter CBT Test

Solve these 10 standard exam-level questions. The system tracks your response time, detects rapid guessing via Cognitive Reading Thresholds, and outputs your post-session diagnosis.

Interactive Practice Progress:0 / 10 Answered

⏱️ Launch Chapter CBT Simulator

Q1Straight Lines & Angle Between Lines

Expected: 60sEasy

If the lines $3x - 4y - 7 = 0$ and $2x - 3y - 5 = 0$ are two diameters of a circle of area $49\pi$ square units, the equation of the circle is :

Q2Circles & Tangents

Expected: 60sEasy

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x − y = 1 and 2x + y = 3 is :

Q3Conic Sections: Parabola, Ellipse, Hyperbola

Expected: 60sEasy

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

Q4Straight Lines & Angle Between Lines

Expected: 60sEasy

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

Q5Circles & Tangents

Expected: 90sMedium

If the equation of the locus of a point equidistant from the point $\left( {{a_{1,}}{b_1}} \right)$ and $\left( {{a_{2,}}{b_2}} \right)$ is $\left( {{a_1} - {a_2}} \right)x + \left( {{b_1} - {b_2}} \right)y + c = 0$ , then the value of $'c'$ is :

Q6Conic Sections: Parabola, Ellipse, Hyperbola

Expected: 90sMedium

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola ${{{x^2}} \over 4} - {{{y^2}} \over 2} = 1$ at the point $\left( {{x_1},{y_1}} \right)$ . Then $x_1^2 + 5y_1^2$ is equal to :

Q7Straight Lines & Angle Between Lines

Expected: 90sMedium

Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?

Q8Circles & Tangents

Expected: 90sMedium

The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is :

Q9Conic Sections: Parabola, Ellipse, Hyperbola

Expected: 120sHard

Let $A = \{ (x,y) \in R \times R|2{x^2} + 2{y^2} - 2x - 2y = 1\}$ , $B = \{ (x,y) \in R \times R|4{x^2} + 4{y^2} - 16y + 7 = 0\}$ and $C = \{ (x,y) \in R \times R|{x^2} + {y^2} - 4x - 2y + 5 \le {r^2}\}$ . Then the minimum value of |r| such that $A \cup B \subseteq C$ is equal to

Q10Straight Lines & Angle Between Lines

Expected: 120sHard

Let $m_{1}, m_{2}$ be the slopes of two adjacent sides of a square of side a such that $a^{2}+11 a+3\left(m_{1}^{2}+m_{2}^{2}\right)=220$ . If one vertex of the square is $(10(\cos \alpha-\sin \alpha), 10(\sin \alpha+\cos \alpha))$ , where $\alpha \in\left(0, \frac{\pi}{2}\right)$ and the equation of one diagonal is $(\cos \alpha-\sin \alpha) x+(\sin \alpha+\cos \alpha) y=10$ , then $72\left(\sin ^{4} \alpha+\cos ^{4} \alpha\right)+a^{2}-3 a+13$ is equal to :

🗺️ Recommended Learning Sequence

Differential Equations➔Coordinate Geometry (Current)➔Vector Algebra & 3D Geometry

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Coordinate Geometry Preparation Hub

What is Coordinate Geometry?

💡 Why Study Coordinate Geometry?

⚠️ Common Pitfalls to Avoid

Coordinate Geometry Theory & Derivations

Important Formulas & Cheat Sheet

Coordinate Geometry Interactive Practice

If the lines 3x−4y−7=03x - 4y - 7 = 03x−4y−7=0 and 2x−3y−5=02x - 3y - 5 = 02x−3y−5=0 are two diameters of a circle of area 49π49\pi 49π square units, the equation of the circle is :

Equation of the tangent to the circle, at the point (1, −1), whose centre is the point of intersection of the straight lines x − y = 1 and 2x + y = 3 is :

The number of integral values of m so that the abscissa of point of intersection of lines 3x + 4y = 9 and y = mx + 1 is also an integer, is :

Axis of a parabola lies along x-axis. If its vertex and focus are at distances 2 and 4 respectively from the origin, on the positive x-axis then which of the following points does not lie on it?

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola x24−y22=1{{{x^2}} \over 4} - {{{y^2}} \over 2} = 14x2​−2y2​=1 at the point (x1,y1)\left( {{x_1},{y_1}} \right)(x1​,y1​). Then x12+5y12x_1^2 + 5y_1^2x12​+5y12​ is equal to :

Consider the set of all lines px + qy + r = 0 such that 3p + 2q + 4r = 0. Which one of the following statements is true?

The locus of the centres of the circles, which touch the circle, x2 + y2 = 1 externally, also touch the y-axis and lie in the first quadrant, is :

🗺️ Recommended Learning Sequence

Ready to achieve complete mastery in Coordinate Geometry?

If the lines $3x - 4y - 7 = 0$ and $2x - 3y - 5 = 0$ are two diameters of a circle of area $49\pi$ square units, the equation of the circle is :

A line parallel to the straight line 2x – y = 0 is tangent to the hyperbola ${{{x^2}} \over 4} - {{{y^2}} \over 2} = 1$ at the point $\left( {{x_1},{y_1}} \right)$ . Then $x_1^2 + 5y_1^2$ is equal to :