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Common Errors Committed by the Students in Secondary Mathematics Errors that students often make in doing secondary mathematics during their practice and during the examinations and their remedial measures are well explained here stp by step. Some Common Errors in Mathematics

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Conic Sections / Ellipse & Hyperbola / Chapter-11 / Class XI

Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics Conic Section, Ellipse and its complete explanation with diagrams, Hyperbola and its complete explanation with diagrams

ELLIPSE An ellipse is the set of all points in a plane sum of whose distances from two fixed points in the plane is a constant. The two fixed points are called foci.

CENTRE OF THE ELLIPSE:- The mid point of the line segment joining the foci is called the centre of the ellipse.

MAJOR AXIS:- A line segment passing through the foci of the ellipse is called the major axis.

MINOR AXIS:- A line passing through the centre of the ellipse and is perpendicular to the major axis is called minor axis.

ECCENTRICITY:- It is defined as the ratio of the half of the distance between the foci to the length of the semi major axis. Mathematically:- e = c / a

LATUS RECTUM:- It is the line segment perpendicular to the major axis through any of the foci and whose end points lie on the ellipse. \[Mathematically:- Length \; of\; latus\; rectum\: \: is\: =\frac{2b^{2}}{a}\]

STANDARD EQUATIONS OF THE ELLIPSE:-

\[When\; major\; axis\; is\; along \; the\; x-axis\; then\; equation \; of \; the\; ellipse\; is\; \frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\]

\[When\; major\; axis\; is\; along \; the\; y-axis\; then\; equation \; of \; the\; ellipse\; is\; \frac{x^{2}}{b^{2}}+\frac{y^{2}}{a^{2}}=1\]\[c^{2}=a^{2}-b^{2}\]

PROPERTIES OF ELLIPSE

HYPERBOLA:-

It is the set of all points in a plane, the difference of whose distances from two fixed points in the plane is fixed or constant.

TRANSVERSE AXIS:- The line through the focuses is called transverse axis. Length of transverse axis is 2a.

CONJUGATE AXIS:- A line through the centre and perpendicular to the transverse axis is called conjugate axis. Length of conjugate axis is 2b

ECCENTRICITY:- The ratio e = c/a is called eccentricity

LENGTH OF LATUS RECTUM:- It is the line segment perpendicular to the transverse axis through any of the focuses and whose end points lie on the hyperbola.

Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics

STANDARD EQUATIONS OF HYPERBOLA:-

\[When\; major\; axis \: \: is\: x-axis\: then \: equation\: of\: hyperbola\: is \: \: \frac{x^{2}}{a^{2}}-\frac{y^{2}}{b^{2}}=1\]\[When\; major\; axis \: \: is\: y-axis\: then \: equation\: of\: hyperbola\: is \: \: \frac{y^{2}}{a^{2}}-\frac{x^{2}}{b^{2}}=1\]

PROPERTIES OF HYPERBOLA

Art Integrated Project on Conic Section Class 11

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Maths Conic Section Part 2 Class 11 NCERT-cbse mathematics

Theorems on Parallelograms Ch-8 Class-IX Explanation of all theorems on Parallelograms chapter 8 class IX, Theorem 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 8.8, 8.9, 8.10, Mid point theorem and its converse. All theorems of chapter 8 class IX. Theorem 8.1: Prove that a diagonal of a parallelogram divides it into two congruent triangles. Given: In Parallelogram ABCD, AC is the diagonal To Prove: △ACD ≌ △ABC Proof: In △ACD and △ABC, ∠1 = ∠2 ......... (Alternate angles ∠3 = ∠4 .......... (Alternate interior angles AC = AC ........ (Common Sides ⇒ By ASA ≌ rule △ACD ≌ △ABC Theorem 8.2: In a parallelogram, opposite sides are equal. Given: ABCD is a parallelogram To Prove : AB = CD and BC = AD Proof: In △ ACD and △ ABC, ∠ 1 = ∠ 2 ......... (Alternate angles ∠ 3 = ∠ 4 .......... (Alternate interior angles AC = AC ........ (Common Sides ⇒ By ASA ≌ rule △ ACD ≌ △ ABC ⇒ AB = CD and BC = AD ….. By CPCT Theorem

E-LESSON PLANNING FOR MATHEMATICS TEACHER CLASS 10TH lesson plan for maths class X cbse, lesson plans for mathematics teachers, Method to write lesson plan for maths class 10, lesson plan for maths class X, lesson plan for mathematics grade X, lesson plan for maths teacher in B.Ed. RESOURCE CENTRE MATHEMATICS LESSON PLAN (Mathematics) : CLASS 10 th Techniques of Making E-Lesson Plan : Click Here Click Here For Essential Components of Making Lesson Plan Chapter 1 : Number System

E- LESSON PLAN SUBJECT MATHEMATICS CLASS 10 lesson plan for maths class 10 cbse lesson plans for mathematics teachers, Method to write lesson plan for maths class 4, lesson plan for maths class 12 rational numbers, lesson plan for mathematics grade 10, lesson plan for maths in B.Ed. TEACHER'S NAME : DINESH KUMAR SCHOOL : RMB DAV CENTENARY PUBLIC SCHOOL NAWANSHAHR SUBJECT : MATHEMATICS CLASS : X STANDARD BOARD : CBSE LESSON TOPIC / TITLE : CHAPTER 13: SURFACE AREA & VOLUME ESTIMATED DURATION: This topic is divided into seven modules and are completed in twelve class meetings. PRE- REQUISITE KNOWLEDGE:- Perimeter and Area: Class VII Visualizing Solid Shapes: Class VII Visualizing Solid Shapes: Class VIII Mensuration: Class VIII Surface Areas and Volumes: Class IX Knowledge of unit conversion in mathematics

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