# Conic Sections Notes, Class 11 Mathematics | SwaVid Conic Sections, NCERT Class 11 Mathematics: notes with key ideas, formulas, common mistakes and 3 quick checks with worked answers. Canonical: https://www.swavid.com/cbse/class-11/maths/chapter/conic-sections Source: https://www.swavid.com/cbse/class-11/maths/chapter/conic-sections # Conic Sections ## Formulas and definitions ## Key ideas ## Common mistakes ## Quick checks ## Keep going ## Questions parents ask ## Class 11 Mathematics on SwaVid ### Sections of a cone ### Circle ### Parabola ### Ellipse ### Hyperbola ### Latus rectum ### Next chapter ### Related chapter ### All chapters SwaVid › CBSE › Class 11 › Mathematics › Conic Sections Notes written by SwaVid from the NCERT textbook. Class 11 Mathematics, Chapter 10. Key ideas, formulas and common mistakes. CBSE does not print marks for a single chapter. Short answer. This chapter covers the curves formed by the intersection of a plane with a double right circular cone, specifically circles, parabolas, ellipses, and hyperbolas. Students learn to derive and apply their standard algebraic equations along with key features like foci, vertices, directrices, and axes. Source: NCERT Mathematics (Reprint 2026-27) , Chapter 10, Conic Sections When a plane cuts a double right circular cone, different curves are obtained depending on the angle made by the plane with the vertical axis. These curves include circles, ellipses, parabolas, and hyperbolas, as well as degenerate cases like points and intersecting lines. A circle is the set of all points in a plane that are equidistant from a fixed point called the centre. The fixed distance is the radius, giving the standard equation (x - h)² + (y - k)² = r² for centre (h, k) and radius r. A parabola is the set of all points in a plane that are equidistant from a fixed line called the directrix and a fixed point called the focus not on the line. The standard equations oriented along coordinate axes are y² = 4ax, y² = -4ax, x² = 4ay, and x² = -4ay. An ellipse is the set of all points in a plane whose distances to two fixed points have a constant sum that is greater than the distance between the two points. The standard form is x²/a² + y²/b² = 1, where a² = b² + c² and eccentricity e = c / a. A hyperbola is the set of all points in a plane where the absolute difference of the distances from two fixed points is constant. The standard form is x²/a² - y²/b² = 1, where c² = a² + b² and eccentricity e = c / a. The latus rectum of a conic section is a chord passing through a focus and perpendicular to the axis of symmetry. Its length is 4a for a parabola, 2b²/a for an ellipse, and 2b²/a for a hyperbola. Try each question first. Then tap it to see the answer. Group terms: (x² - 4x) + (y² + 6y) = 12 Complete the square: (x - 2)² - 4 + (y + 3)² - 9 = 12 (x - 2)² + (y + 3)² = 12 + 4 + 9 = 25 = 5² Compare with (x - h)² + (y - k)² = r² to get h = 2, k = -3, r = 5 Centre = (2, -3), radius = 5 Compare y² = -12x with the standard form y² = -4ax 4a = 12, so a = 3 The parabola opens along the negative x-axis, so the axis is the x-axis (y = 0) Focus = (-a, 0) = (-3, 0) Length of latus rectum = 4a = 12 Focus = (-3, 0), axis is y = 0, length of latus rectum = 12 Identify a² = 25 and b² = 9, so a = 5 and b = 3 Since a² is under x², the major axis is along the x-axis Calculate c² = a² - b² = 25 - 9 = 16, so c = 4 Foci = (±c, 0) = (±4, 0) Eccentricity e = c / a = 4 / 5 Foci = (±4, 0), e = 4/5 Introduction to Three Dimensional Geometry . Straight Lines . The 14 chapters of Class 11 Mathematics . The CBSE Class 11 Maths curriculum says it gives no chapter or unit-wise weightage. Theory is 80 marks, plus 20 for internal assessment. No. They are written by SwaVid from the NCERT textbook. The CBSE curriculum is the reference for what is assessed. Introduction to Three Dimensional Geometry. SwaVid is an AI tutor for Indian students in Classes 6 to 12. It finds the earlier ideas a child missed, then teaches today’s chapter. Start free to see how it works. - Ch 10 NCERT book - 80 marks, theory paper - 3 quick checks - Mixing up the relation between a, b, and c for ellipses and hyperbolas . For an ellipse, a is the largest semi-axis so a² = b² + c². For a hyperbola, the foci are farther out so c² = a² + b². - Assigning the major axis incorrectly when the larger denominator is under y² . Check which denominator is larger in an ellipse. If y² has the larger denominator a², the major axis lies along the y-axis, giving foci at (0, ±c). - Identifying a and b in a hyperbola based on which denominator is larger . In a hyperbola, a² is always under the positive term regardless of magnitude. The negative term determines b². - Writing the wrong sign for the coordinates of a circle's centre . Remember the standard form has minus signs: (x - h)² + (y - k)² = r². For (x + 3)² + (y - 4)² = 25, the centre is (-3, 4), not (3, -4). ## Key Links - [CBSE](https://www.swavid.com/cbse) - [Class 11](https://www.swavid.com/cbse/class-11) - [Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup) - [All 14 chapters](https://www.swavid.com/cbse/class-11/maths/chapters) - [NCERT Mathematics (Reprint 2026-27)](https://ncert.nic.in/textbook.php) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/introduction-to-three-dimensional-geometry) - [Open notes](https://www.swavid.com/cbse/class-11/maths/chapter/straight-lines) - [Class 11 Mathematics](https://www.swavid.com/cbse/class-11/maths/chapters) - [Start free →](https://www.swavid.com/signup)