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333202 1002.qxd 12/8/05 9:00 AM Page 735 Section 10.2 Introduction to Conics: Parabolas 735 10.2 Introduction to Conics: Parabolas What you should learn Recognize a conic as the intersection of a.

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The standard form of a horizontal parabola is (y - k)2 = 4p(x - h), where the focus is given by the point (h + p, k). For example, the parabola (y - 4)2 = 4(x - 1) has a focus of (2, 4) since our h equals 1, our p equals 1 and our k equals 4. Our p equals 1 since we have a 4 in the 4p place, and 4 times 1 will equal 4.

0:00 6:30 And finally we have the factored form. And these values R1 and R2 are the roots of the equation. AndMoreAnd finally we have the factored form. And these values R1 and R2 are the roots of the equation. And it would show where for instance the graft crossed the x-axis if it were to have x-intercepts.

The general equation of a parabola is: y = a(x-h)2 + k or x = a(y-k)2 +h, where (h,k) denotes the vertex. The standard equation of a regular parabola is y2 = 4ax.

Ax2+Bxy+Cy2+Dx+Ey+F=0 where A,B,C,D,E and F are constants. As we change the values of some of the constants, the shape of the corresponding conic will also change. It is important to know the differences in the equations to help quickly identify the type of conic that is represented by a given equation.

If a parabola has a vertical axis, the standard form of the equation of the parabola is this: (x - h) [ 2 ] = 4p(y - k), where p≠ 0. The vertex of this parabola is at (h, k). The focus is at (h, k + p).

Conic Sections Equations Conic section NameEquation when the centre is at the Origin, i.e. (0, 0) Circle x2 + y2 = r2; r is the radius Ellipse (x2/a2) + (y2/b2) = 1 Hyperbola (x2/a2) – (y2/b2) = 1 Parabola y2 = 4ax, where a is the distance from the origin to the focus

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