Problem of the Day Sketch a graph of the equation. 1. (x ­ 2)2 + (y ­ 1)2 = 4 2. Problem of the Day Sketch a graph of the equation. 1. 16(x ­ 1)2 ­ 9(y + 2)2 = 144 Problem of the Day Write the equation. Ellipse with center (4,5), major axis length 10 and a focus at (6,5) Hyperbola with center (­1, 2), conjugate axis length 16, and a transverse axis length 8 and along the line y = 2 Problem of the Day Write the equation of the conic section in standard form x2 + y2 ­ 10x + 4y ­ 7 = 0 4x2 + y2 ­ 8x + 4y ­ 4 = 0 Standard Equations of Translated Conic Sections Hyperbolas Hyperbolas Transverse Axis Conjugate Axis Foci Graph the following conic section. Graph the following conic section. Find the coordinates of the foci. Find the length of the transverse and conjugate axes. Graph the following conic section. Find the coordinates of the foci. Find the length of the transverse and conjugate axes. Use completing the square to write the equation of the hyperbola in standard form. y2 ­ 4x2 + 8x ­ 2y = 67 5x2 ­ y2 + 30x ­ 4y = 84 Use completing the square to write the equation of the hyperbola in standard form. Then find the coordinates of the foci. x2 ­ 9y2 + 16x ­ 72y ­ 161 = 0 Use completing the square to write the equation of the hyperbola in standard form. Then find the coordinates of the foci. 8y2 ­ 7x2 ­ 32y + 42x ­ 87 = 0 Write the equation of the hyperbola using the following information. Center (5,6), Vertex at (9,6) and conjugate axis length 10 Vertices (­4,­1) and (­4,­5) and Foci (­4,0) and (­4,­6) Standard Equations of Translated Conic Sections Parabolas (y ­ k)2 = 4a(x ­ h) (x ­ h)2 = 4a(y ­ k) Circle (x ­ h)2 + (y ­ k)2 = r2 Ellipses Translation of Axes Identify the conic section as a parabola, circle, ellipse, or hyperbola based on the equation. 1. 4x2 + 5y2 = 20 2. x2 ­ 4 = 2y 3. 6y2 ­ 2x = 8 4. 9x2 ­ y2 = 45 5. 12x2 + 12y2 = 24 6. Write the equation in standard form. Then identify the conic section. 1. 16(x ­ 4)2 ­ 4y2 = 64 2. 3(y ­ 1)2 = 24(x + 2) 3. 5(x ­ 3)2 + 5y2 = 125 Write the equation in standard form and identify 4x2 + y2 ­ 16x + 6y ­ 11 = 0 x2 ­ 8x ­ 12y ­ 24 = 0 Write the standard form of the equation Parabola with vertex(­7,3) and focus (­9,3) Circle with center (­5, 9) and radius 7 Review Problems Find the foci for the ellipse with major axis on the line y = 2 and length 12. The minor axis is on the line x = ­2 and has length 8. Find the equation of the hyperbola with vertices (2,­3) and (6,­3) with foci at (­2,­3) and (10,­3). Review Problems Find the foci for the hyperbola with transverse axis on the line y = ­5 and length 6. The conjugate axis is on the line x = 2 and has length 10. Find the equation of the ellipse with vertices (4,­7) and (4,3) with foci at (4,­6) and (4,2). Write the equation in standard form and sketch a graph x2 ­ 4x + 4y = 0 x2 + y2 ­ 6x + 18y ­ 10 = 0 Graph the following conic sections. Find the coordinates of the foci. pgs 892­893:15­21,25­31.