My College Books

Problems On Hyperbola HYPERBOLA BY  A POINT OF KNOWN CO-ORDINATES, P-V DIAGRAM, AND BY DIRECTRIX FOCUS METHOD. HYPERBOLA BY A POINT OF KNOWN CO-ORDINATES... 1. Point P is 40 mm and 30 mm from horizontal and vertical axes respectively. Draw Hyperbola through it. SOLUTION STEPS: Extend the horizontal line from P to the right side. Extend vertical line from P upward. On horizontal line from P, mark some points taking any distance and name them after P-1,2,3,4 etc. Join 1-2-3-4 points to pole O.Let them cut part [P-B] also at 1,2,3,4 points. From horizontal 1,2,3,4 draw vertical lines downwards From vertical 1,2,3,4 points [from P-B] draw horizontal lines. Line from 1 horizontal and line from 1 vertical will meet at P 1 . Similarly mark P 2 , P 3 , P 4 points. Repeat the procedure by marking four points on an upward vertical line from P and joining all those tp pole O. Name these points P 6 , P 7 , P 8 , etc, and join them by a smooth curve. HYPERBOLA BY P-V DIAGRA...

 PARABOLA BY RECTANGLE METHOD, METHOD OF TANGENTS AND DIRECTRIX-FOCUS METHOD.  RECTANGLE METHOD... 1. A ball thrown in air attains 100 m height and covers horizontal distance 150 m on the ground. Drew the path of the ball(projectile). STEPS: Draw a rectangle of the above size and divide it into two equal vertical parts Consider left part fir construction divide height and length in an equal number of parts and name those 1,2,3,4,5 & 6 Join vertical 1,2,3,4,5 & 6 to the top center of the rectangle similarly draw upward vertical lines form horizontal 1,2,3,4,5 and wherever these lines intersect previously drawn inclined lines in sequence mark those points and further join in smooth possible curve. Repeat the construction on the right side rectangle also. Join all sequence. This locus is parabola.   METHOD OF TANGENTS... 2. Draw an isosceles triangle of 100 mm long base and 110 mm long altitude, Inscribe a parabola in it by method of tangents. SOLUTION STEPS: Con...

 Problems On Ellipse ELLIPSE BY CONCENTRIC CIRCLE METHODE, RECTANGLE METHOD, OBLONG METHOD, ARCS OF CIRCLE METHOD, RHOMBUS METHOD AND BY DIRECTRIX-FOCUS METHOD.   ELLIPSE BY CONCENTRIC CIRCLE METHODE...  1 ] Draw ellipse by concentric circle method take, take major axis 100 mm and minor axis 70 mm long.  steps:  Draw both axes as perpendicular bisector of each other & give name their ends as shown. Taking their intersecting points as a center, Draw two concentric circles considering both as respective diameters. DIvide both circle in 12 equal parts & name as shown. From all the point outer circle draw a vertical line downwards and upwards respectively. From all the points in the inner circle draw a horizontal line to intersection those vertical lines. mark all intersecting points properly as those are the points on the ellipse. Join all these points along with the end of both axes in a smooth possible curve. it is required ellipse. ELLIPSE BY RECTANGLE MET...

Engineering Curves Part I Conic Section Ellipse, Parabola and Hyperbola are called conic sections because these curves appear on the surface of a cone when it is cut by some typical cutting planes. observe illustrations given below...   Common definition of  parabola ellipse and hyperbola: these are the locus of points moving in a plane such that the ratio of it' s distances from s fixed point (focus) and the fixed line( directrix) always remains constant. the ratio is called ECCENTRICITY. ( e ) For Ellipse E < 1     For Parabola E = 1       For Hyperbola E > 1 Parabola: A parabola is a plane curve where any point is at an equal distance from a fixed point ( the focus ) and a fixed straight line ( the directrix ). Ellipse: It is a locus of a point moving in a plane such that the sum of it' s distance from two fixed points always remains constant. And this sum equals to the length of a major axis. These two fixed points are FOCUS 1 & FOCUS 2. Hyperbola: Hyperbola is a...