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Boards Concepts Booster Class 11 Hyperbola

Class 11 Hyperbola Concept Booster for Board Exam. Students can study from this comprehensive conceptual PDfs and videos on hyperbola and its various sub-topics for effective board exam preparation. The concept booster helps the student to swiftly revise the important concepts just before the board exam.<br>For more such video solutions/Pdf solution, visit https://doubtnut.com and clear your doubt instantly.

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Boards Concepts Booster Class 11 Hyperbola

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  1. BOARDS CONCEPTS BOOSTER HYPERBOLA  Download Doubtnut Today Ques No. Question CONCEPT FOR BOARDS || Chapter HYPERBOLA 1. INTRODUCTION 1 1. Analytical definition of hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 1. INTRODUCTION 2 2. Equation of hyperbola in standard form  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 1. INTRODUCTION 3 3. Various results of hyperbola  Click to LEARN this concept/topic on Doubtnut

  2. CONCEPT FOR BOARDS || Chapter HYPERBOLA 1. INTRODUCTION 4 4. Rectangular or equilateral Hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 1. INTRODUCTION 5 5. Difference of Focal radii of any point is equal to the length of major axis  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 2. POSITION OF POINTS WITH RESPECT TO A HYPERBOLA 6 1. Position of a point with respect to hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 3. CONJUGATE HYPERBOLA 7 1. Conjugate hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 3. CONJUGATE HYPERBOLA 8 2. Comparison of Hyperbola and its conjugate hyperbola

  3.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 4. AUXILIARY CIRCLE AND ECCENTRIC ANGLE 9 1. Auxiliary Circle and eccentric angle  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 4. AUXILIARY CIRCLE AND ECCENTRIC ANGLE 3. Relation between equation of Hyperbola and major minor axis when axis is not parallel to co ordinate axes 10  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 5. INTERSECTION OF A LINE AND HYPERBOLA 11 1. Intersection of line and hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 5. INTERSECTION OF A LINE AND HYPERBOLA 12 2. Director Circle of hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 6. EQUATION OF TANGENT TO HYPERBOLA

  4. 13 1. Equation of tangent at hyperbola at point and (x1,y1) (asecθ,b tanθ)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 6. EQUATION OF TANGENT TO HYPERBOLA 14 2. Point of contact when line touches the hyperbola y = mx + c  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 6. EQUATION OF TANGENT TO HYPERBOLA 15 3. Point of intersection of tangents at points and P(α) Q(β)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 6. EQUATION OF TANGENT TO HYPERBOLA y2 x2 4. P is a point on the hyperbola ; N is a foot of perpendicular from P = 1 − 16 a2 b2 on the transverse axis . The tangent to hyperbola at P meets the transeverse axis at T . If O is the center of the hyperbola ; then find the value of . OT × ON  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 7. EQUATION OF NORMAL TO THE HYPERBOLA 17 1. Equation of normal of hyperbola  Click to LEARN this concept/topic on Doubtnut

  5. CONCEPT FOR BOARDS || Chapter HYPERBOLA 7. EQUATION OF NORMAL TO THE HYPERBOLA 18 2. Some important points related to equation of normal to hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 8. CHORDS AND CHORDS OF CONTACT 19 1. Equation of chord joining points and P(α) Q(β)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 8. CHORDS AND CHORDS OF CONTACT 2. If x2 and are the ends of the focal chord of (a secθ,b tanθ) y2 (asecϕ,btanϕ) then prove that = 1 − a2 b2 20

  6. ϕ θ tan( )tan( ) 2 2 1 − e = 1 + e  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 8. CHORDS AND CHORDS OF CONTACT 21 3. Equation of chord whose midpoint is (x1,y1)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 9. ASSYMPTOTES OF HYPERBOLA 22 1. What are assymptotes of hyperbola ?  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA y2 x2 1. If the angles between assymptotes of hyperbola is then − = 1 2θ 23 a2 b2 e = secθ  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA

  7. 24 2. A hyperbola and its conjugate have the same asymptotes  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA 25 3. The assymptotes pass through the centre of the hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA 4. The perpendicular from the foci on either asymptote meets it at the same point as the corresponding directrix and the common points of intersection lie on the auxiliary circle 26  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA 5. If from any points on the asymptotes, a straight line is drawn perpendicular to the transverse axis , the product of the segments of this line intercepted between the point and the curve is always equal to the square of the semi conjugate axis. 27  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA 6. If a hyperbola passing through the origin has as its asymptotes then find the equations of its transverse and conjugate axes and 3x − 4y − 1 = 0 28 4x − 3y − 6 = 0

  8.  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 10. SOME IMPORTANT POINTS OF ASSYMPTOTES OF HYPERBOLA 7. Find the equations of the asymptotes of the hyperbola 3x2+ 10xy + 8y2 29 + 14x + 22y + 7 = 0  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 30 1. Rectangular hyperbola : xy = c2  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 31 2. Important results of rectangular hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 32 3. Equation of tangent of rectangular hyperbola  Click to LEARN this concept/topic on Doubtnut

  9. CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 33 4. Equation of normal of rectangular hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 34 5. Equation of chord with middle point as (h,k)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 6. A triangle has its vertices on a rectangular hyperbola . Prove that the orthocenter of the triangle also lies on the same hyperbola. 35  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 11. RECTANGULAR HYPERBOLA 36 7. Concyclic points on rectangular hyperbola  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA

  10. 37 1. The eccentricity of rectangular hyperbola is √2  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 38 2. The parametric form of rectangular hyperbola xy = c2  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 39 c c 3. The Slope of the chod joining point P and (ct1; ) Q(ct2; ) t1 t2  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 40 c 4. The slope of tangent at point is (ct, ) t  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 41 5. The equation of tangent at point whose parameter is t  Click to LEARN this concept/topic on Doubtnut

  11. CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 42 6. The equation of normal at point whose parameter is t  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 43 7. The equation of tangent at (x1,y1)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 12. PROPERTIES OF RECTANGULAR HYPERBOLA 44 8. The chord with a given middle point as (h, k)  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 13. POLE AND POLAR 45 1. Show that the line touches the hyperbola 4x2− 9y2= 27 4x − 3y = 9  Click to LEARN this concept/topic on Doubtnut CONCEPT FOR BOARDS || Chapter HYPERBOLA 13. POLE AND POLAR 2

  12. 46 2 2. The length of conjugate axis of a hyperbola is 8 and its asymptotes are y = x 3 2 and . find the equation of hyperbola and its ecentricity y = − x 3  Click to LEARN this concept/topic on Doubtnut  Download Doubtnut to Ask Any Math Question By just a click  Get A Video Solution For Free in Seconds  Doubtnut Has More Than 1 Lakh Video Solutions  Free Video Solutions of NCERT, RD Sharma, RS Aggarwal, Cengage (G.Tewani), Resonance DPP, Allen, Bansal, FIITJEE, Akash, Narayana, VidyaMandir  Download Doubtnut Today

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