Find the standard form of ? + 2x - 4+1 = 0(Remember that the conic section formulas are given at the top of this exam). 0 (x + 1)² – (y – 1)² = 0 O(x + 1)² =y 0 (x + 1)2 = y-1 0 (x + 1)² -% =0
Find the standard form of the ellipse that has foci at (+12,0) and vertices at (+13,0). (Remember that the conic section formulas are given at the top of this exam). + = 1 13 o + 1 169 O + = 1 + y? 169 1 25
Select the equation that results in the following graph of a conic section (Remember that the conic section formulas are given at the top of this exam). 3+ 21 1+ x -1 O (2-2) (y+1) 1 9 4 O(x-2) 9 (y+1) + 1 O (2-2) + 1 O (2-2) (+1) 9
Select the equation that results in the following graph of a conic section (Remember that the conic section formulas are given at the top of this exam). 3. 27 -2 -1 -1+ -2+ -3+ 0 (x - 2)2 = 1(y+1) O (y + 1)² = 1 (x - 2) (y - 1)2 = 1(x + 2) 0 (x + 2)= 1(y - 1)
(6) Consider the 3-D conic section 5x2 + y2 + 222-412-y+1+2-1-0. Rotate and translate the coordinate axes to write it in standard form. Hence determine the type of surface this describes (6) Consider the 3-D conic section 5x2 + y2 + 222-412-y+1+2-1-0. Rotate and translate the coordinate axes to write it in standard form. Hence determine the type of surface this describes
Question 27 4 pts Find the partial derivative. Let z = f(x,y) = 9x2 - 11xy + 4yº. Find -11x + 12y -11x - 12y 18x - 1ly 18x +11y2
Question 15 O pts Each equation below represents a conic section. Write the name of the corresponding type of conic. Explain how you know if it is a circle, ellipse, hyperbola or parabola. a) 1 25 9 b) y2 + 6y + x - 6 = 0 c) x² + y2 100 a) ? 9 b) y? – 6y + 2 – 6 – 0 c).x2 + y2 100
2-5 1. Find the Domain of the function and identify any asymptotes (6 pts.) 3. Find the equation of an ellipse with vertices (0, 2) and (8, 2) and a minor axis length of length 6. (3 pts.) (@ y"3x - 1 (6) S(x)- (c) "(x)=-**-***10 4. Graph the conic and identify the type of conic, the center, vertices, and foci, if applicable.(8 pts.) (9251 2. Identify any x-intercepts; y-intercepts and asymptotes of the graph of the function. Then sketch...
d2y d2y dy +6 da2 (h) +13y 2sin x +9y = 18x -+3 +6 dx da d2y (i) d2y (j d2 18x3 4y = 2 sin x dæ2 d2y ,dy .dy 9y 9x2 +21x - 10 dc (k) (1)2 7 + - 4y = e-4x +6 'da2 da2 d2y dy dy (m) 2 dæ2 (n) 4 7y= e 6 cos x 9y = 4e-3r dr2 dr dx d2y d2y (p*) dy + da2 dy (o* 2a COS I 2y 2...
(6) Consider the 3-D conic section 5x2 + y2 + 2,2-4m-y+x+2+1-0. Rotate and translate the coordinate axes to write it in stanHlard form. Hence determine the type of surface this describes (6) Consider the 3-D conic section 5x2 + y2 + 2,2-4m-y+x+2+1-0. Rotate and translate the coordinate axes to write it in stanHlard form. Hence determine the type of surface this describes