open plane curve formed by the intersection of a cone with a plane parallel to its side Hyperbola: a symmetrical open curve formed by the intersection of a circular cone with a plane at a smaller angle with its axis than the side of the cone. Ellipse: a regular oval shape‚ traced by a point moving in a plane so that the sum of its distances from the foci is constant Writing Conics are found everywhere in the world. You may not recognize them at first but they are all around us. Conics can be
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10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface © The McGraw-Hill Companies‚ Inc. Permission required for reproduction or display. Slide 1 10.6 SURFACES IN SPACE EXAMPLE 6.1 Sketching a Surface Solution Since there are no x’s in the equation‚ the trace of the graph in the plane x = k is the same for every k. This is then a cylinder whose trace in every plane parallel to the yz-plane is the parabola z = y2. © The McGraw-Hill Companies‚ Inc. Permission required for
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answer y-coordinate of the centroid answer Problem 707 Determine the centroid of the quadrant of the ellipse shown in Fig. P-707. The equation of the ellipse is . Solution 707 HideClick here to show or hide the solution Equation of ellipse in y as a function of x Differential area Area of quarter ellipse x-coordinate of the centroid answer y-coordinate of the centroid
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Equation of a circle with centre at origin and radius r is PARABOLA( Symmetric about its axis) Right Equation Axis Figure y=0 Left y= 0 Upward x= 0 ) Downward x= 0 Focus (a‚ 0) (-a‚ 0) Vertex (0‚0) (0‚0) Latus 4a 4a Rectum Directrix x = -a x=a ELLIPSE ( Symmetric about both the axis) Equation Equation of the major axis Length of major axis Length of minor axis Vertices Foci Eccentricity Latus Rectum y=0 2a 2b ( a‚ 0) ( c‚ 0) (0‚ a) (0‚0) 4a y = -a (0‚ -a) (0‚0) 4a y =a x=0 2a 2b (0‚ a ) (0
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x=cos(t) y=sin(t) soln:>> theta=linspace(0‚2*pi‚100); >> x=cos(t); y=sin(t); >> plot(x‚y) 7. parabola x=at^2 y=2at t-varies(-4‚4) soln:t=linspace(-4‚4); >> a=1; >> x=a.*t.*t; >> y=2.*a.*t; >> plot(x‚y) 8. hyperbola 9. ellipse An ellipse can be defined as the locus of all points that satisfy the equations x
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Lab 4: Kepler’s Laws (answer sheet) 1. a: semi-major axis b: semi-minor axis c: focus d: center 2. The distance from the center to a focus is 31 millimeters and the length of the semi-major axis is also in millimeters. The numbers are not even and cannot be simplified any further than what they are since 31 is a prime number. The number is 31/102‚ or 31 divided by 102 which results in 0.303921568627451. 3. Kepler’s first Law is that all planets orbit in an elliptical (egg
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equal in area to the square on KL‚ the other side of this rectangle may be precisely superposed upon the latus rectum‚ ZT. This property constitutes the best practical definition of the parabola. If a similar construction were made in the case of the ellipse‚ the side of the rectangle would fall short of the latus rectum; in the case of the hyperbola‚ would surpass it. The modern scientific definition of the parabola is that it is that plane curve of the second order which is tangent to the line at infinity
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distance formula‚ this is not just used in Math but also in Physics‚ Science and many other fields. Journal for the Month of July WHAT I LEARNED? This month‚ I learned that there are also ‘other’ versions of circles. Namely: Parabola Ellipse Hyperbola WHAT IS THE HARDEST TOPIC? For me there was no hard topic because I make sure that I made an effort in understanding the topics before the day ended. HOW I LEARNED? I made sure that I master these topics before there was a summative
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astronomy. Planets orbit the sun. The sun does not orbit the planets. He posed a question of the planetary motion. Later‚ Newton took to answer. Kepler also came across the paths of planets. Their path was elliptical‚ not circular. Planets move in ellipses with the sun at one focus. Prior to this in 1602‚ Kepler found from trying to calculate the position of the Earth in its orbit that as it sweeps out an area defined by the Sun and the orbital path of the Earth that the radius vector describes equal
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larger than who he really is. Iva Rhiana C. Santiago LG 4218 APOLLONIUS OF PERGA As what I have researched‚ Apollonius of Perga was a Greek geometer and astronomer noted for his writings in the conic section. It was him who gave the ellipse‚ the parabola‚ and the hyperbola the names by which we know them. And these things are our lessons this term. The work of Apollonius of Perga has had such a great impact
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