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Question : Graph the ellipse. 19) ((x - 2)^2/9) + ((y + 1)^2/4) = 1 : 2151871

Graph the ellipse.

19) ((x - 2)^{2}/9) + ((y + 1)^{2}/4) = 1

A)

B)

C)

D)

20) ((x - 1)^{2}/4) + ((y + 2)^{2}/9) = 1

A)

B)

C)

D)

21) 4(x - 2)^{2} + 16(y - 1)^{2} = 64

A)

B)

C)

D)

22) 16(x + 1)^{2} + 4(y + 2)^{2} = 64

A)

B)

C)

D)

Find the foci of the ellipse whose equation is given.

23) ((x + 1)^{2}/36) + ((y + 3)^{2}/16) = 1

A) foci at (-1 + 2√(5), -3) and (-1 - 2√(5), -3)

B) foci at (- 2√(5), -3) and (2√(5), -3)

C) foci at (-3 + 2√(5), -1) and (-3 - 2√(5), -1)

D) foci at (-1 + 2√(5), -1) and (-1 - 2√(5), -1)

24) ((x + 2)^{2}/25) + ((y - 3)^{2}/36) = 1

A) foci at (2, 3 - √(11)) and (2, 3 + √(11))

B) foci at (-1, 3 - √(11)) and (-1, 3 + √(11))

C) foci at (-2, 3 - √(11)) and (-2, 3 + √(11))

D) foci at (3, -2 - √(11)) and (3, -2 + √(11))

25) 9(x - 3)^{2} + 36(y - 1)^{2} = 324

A) foci at (3 + 3√(3), 3) and (3 - 3√(3), 3)

B) foci at (- 3√(3), 1) and (3√(3), 1)

C) foci at (3 + 3√(3), 1) and (3 - 3√(3), 1)

D) foci at (1 + 3√(3), 3) and (1 - 3√(3), 3)

26) 36(x - 3)^{2} + 25(y + 3)^{2} = 900

A) foci at (-3, 3 - √(11)) and (-3, 3 + √(11))

B) foci at (3, -3 - √(11)) and (3, -3 + √(11))

C) foci at (-3, -3 - √(11)) and (-3, -3 + √(11))

D) foci at (4, -3 - √(11)) and (4, -3 + √(11))

Convert the equation to the standard form for an ellipse by completing the square on x and y.

27) 9x^{2} + 36y^{2} + 18x + 144y - 171 = 0

A) ((x + 1)^{2}/9) + ((y + 2)^{2}/36) = 1

B) ((x - 1)^{2}/36) + ((y - 2)^{2}/9) = 1

C) ((x + 2)^{2}/36) + ((y + 1)^{2}/9) = 1

D) ((x + 1)^{2}/36) + ((y + 2)^{2}/9) = 1

28) 25x^{2} + 4y^{2} + 100x - 8y + 4 = 0

A) ((x - 2)^{2}/4) + ((y + 1)^{2}/25) = 1

B) ((x + 2)^{2}/4) + ((y - 1)^{2}/25) = 1

C) ((x - 1)^{2}/4) + ((y + 2)^{2}/25) = 1

D) ((x + 2)^{2}/25) + ((y - 1)^{2}/4) = 1

Solve the problem.

29) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 40 feet and the height of the arch over the center of the roadway is 12 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 11 feet and Truck 2 has an overall height of 10 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Truck 1 can pass under the bridge, but Truck 2 cannot.

B) Both Truck 1 and Truck 2 can pass under the bridge.

C) Neither Truck 1 nor Truck 2 can pass under the bridge.

D) Truck 2 can pass under the bridge, but Truck 1 cannot.

30) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 32 feet and the height of the arch over the center of the roadway is 14 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 12 feet and Truck 2 has an overall height of 13 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Both Truck 1 and Truck 2 can pass under the bridge.

B) Truck 2 can pass under the bridge, but Truck 1 cannot.

C) Neither Truck 1 nor Truck 2 can pass under the bridge.

D) Truck 1 can pass under the bridge, but Truck 2 cannot.

31) The arch beneath a bridge is semi-elliptical, a one-way roadway passes under the arch. The width of the roadway is 36 feet and the height of the arch over the center of the roadway is 9 feet. Two trucks plan to use this road. They are both 12 feet wide. Truck 1 has an overall height of 9 feet and Truck 2 has an overall height of 8 feet. Draw a rough sketch of the situation and determine which of the trucks can pass under the bridge.

A) Neither Truck 1 nor Truck 2 can pass under the bridge.

B) Truck 1 can pass under the bridge, but Truck 2 cannot.

C) Truck 2 can pass under the bridge, but Truck 1 cannot.

D) Both Truck 1 and Truck 2 can pass under the bridge.

Find the solution set for the system by graphing both of the system's equations in the same rectangular coordinate system and finding points of intersection.

32) (x^{2} + y^{2} = 9)(9x^{2} + 4y^{2} = 36)

A) {(3, 0), (-3, 0)}

B) {(0, 3), (0, -3)}

C) {(0, 2), (0, -2)}

D) {(2, 0), (-2, 0)}

33) ((x^{2}/25) + (y^{2}/4) = 1)(y = 2)

A) {(0, 2), (0, -2)}

B) {(2, 0)}

C) {(2, 2)}

D) {(0, 2)}

34) (x^{2} + y^{2} = 61)(x + y = -11)

A) {(5, 6), (6, 5)}

B) {(-5, -6), (-6, -5)}

C) {(-5, 6), (-6, 5)}

D) {(5, -6), (6, -5)}

Graph the semi-ellipse.

35) y = - √(16 - 9x^{2} )

A)

B)

C)

D)