# GRAPHING HELP ASAP!!! TEST TOMORROW!!!!! 4/22/11

A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectum
x^2-4x-2y=0

B) sketch the following ellipse. Indicate on the graph the center,verties, foci and end points of the minor axis
9(x-3)^2+(y+2)^2=9

### Comments for GRAPHING HELP ASAP!!! TEST TOMORROW!!!!! 4/22/11

 Apr 22, 2011 Graphing Help - Parabola by: Staff The question: A) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectumx^2-4x-2y=0B) sketch the following ellipse. Indicate on the graph the center,verties, foci and end points of the minor axis9(x-3)^2+(y+2)^2=9The answer:B) sketch the following ellipse. Indicate on the graph the center,verties, foci and end points of the minor axis9(x-3)^2+(y+2)^2=9To view B), click the following link:http://www.solving-math-problems.com/graphing-help.htmlA) Determine the standard form of the following parabola. Identify the vertex, focus point, directrix and points of the latus rectumx^2-4x-2y=0the equation for the standard form of a parabola is:y = a(x – h)² + kThe general equation is: y = ax² + bx + cConvert the equation in A) to standard form:x² - 4x - 2y = 0x² - 4x - 2y + 2y = 0 + 2yx² - 4x + 0 = 0 + 2yx² - 4x = 0 + 2yx² - 4x = 2y2y = x² - 4x 2y/2 = (x² - 4x)/2y * (2/2) = (x² - 4x)/2y * (1) = (x² - 4x)/2y = (x² - 4x)/2y = x²/2 - 4x/2y = x²/2 - (4/2)* xy = x²/2 - (2)* xy = x²/2 – 2xy = a(x – h)² + kthe standard form for A) is:y = a(x – h)² + ky = (1/2) * (x – 2)² - 2the vertex is: (h,k)for this equation, the vertex is: (2,-2)the focal point of the parabolafocus: (h, k + p)the conic form of the equation is:(y - k)² = 4p(x – h)y = (1/2) * (x – 2)² - 2y + 2= (1/2) * (x – 2)² - 2 + 2y + 2= (1/2) * (x – 2)² (y + 2)*2= 2*(1/2) * (x – 2)² 2*(y + 2) = (x – 2)² (x – 2)² = 2*(y + 2)4p = 2p = ½focus: (h, k + p) = (2, -2 + ½) = (2, -1.5) directrix: y = k - p = -2-1/2 = -2.5latus rectumthe length of the latus rectum = 4p = 4*(1/2) = 2 The parabola is shown in the following graph (click link to view, use the Backspace key to return to this page):http://www.solving-math-problems.com/images/parabola-graph.pngThanks for writing.Staff www.solving-math-problems.com

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