Circle Class 11 Notes | Formulae | Equations of Circle - IIT JEE
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eSaral provides detailed Notes of Physics, Chemistry, Mathematics, and Biology for classes 11, and 12. So here you will get class 11 notes for mathematics. There are important points in Mathematics such as formulae, equations, identities, properties, theorems, etc. what has to be remembered to solve problems in Math.eSaral is providing complete study material to prepare for IIT JEE, NEET and Boards Examination. So here Circle Class 11 Notes with Important Questions for IIT JEE Exam preparation. With the help of Notes, candidates can plan their Strategy for a particular weaker section of the subject and study hard. So, go ahead and check the Important Notes for CBSE Class 11 Maths.
India's Best Exam Preparation for Class 11th - Download Now
Circle Class 11 Notes
India's Best Exam Preparation for Class 11th - Download Now
India's Best Exam Preparation for Class 11th - Download Now
India's Best Exam Preparation for Class 11th - Download Now
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India's Best Exam Preparation for Class 11th - Download Now
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Frequently Asked Questions
Find answers to common questions.
What is the condition for a line to be tangent to a circle?
A line y = mx + c is tangent to the circle x² + y² = r² if the perpendicular distance from the centre to the line equals the radius, i.e., r/√(1 + m²) = c or equivalently c² = r²(1 + m²). This condition is used directly in JEE problems to find the value of unknown constants.
How do I find the centre and radius from the general equation of a circle?
From the general equation x² + y² + 2gx + 2fy + c = 0, the centre is (−g, −f) and the radius is √(g² + f² − c). Complete the square for x and y terms to verify. Always check that g² + f² − c > 0; otherwise the circle is imaginary or a single point.
What is the standard equation of a circle in Class 11?
The standard equation of a circle with centre (h, k) and radius r is (x − h)² + (y − k)² = r². When the centre is at the origin, this simplifies to x² + y² = r². This form is the most direct way to identify the centre and radius of a circle and is the basis for all other forms.
What is the diameter form of a circle and when should I use it?
The diameter form is (x − x₁)(x − x₂) + (y − y₁)(y − y₂) = 0, used when the two endpoints of a diameter (x₁, y₁) and (x₂, y₂) are given. It is derived from the property that any angle subtended in a semicircle is 90°. This is faster than computing the centre and radius separately.
How many marks do circles carry in JEE Main?
Circles typically appear in 1–2 questions in JEE Main, contributing approximately 4–8 marks per session. The NTA syllabus places circles under Coordinate Geometry, and questions often combine circles with straight lines or other conics. Consistent practice of tangent-normal and family-of-circles problems gives the highest return on study time.
What is the radical axis of two circles?
The radical axis of two circles S₁ = 0 and S₂ = 0 is the locus of points from which the tangent lengths to both circles are equal. Its equation is S₁ − S₂ = 0, which is always a straight line. The radical axis is perpendicular to the line joining the two centres, regardless of whether the circles intersect.