Math23x Exit Exam Review Material - Analytic Geometry

MATH23X EXIT EXAM REVIEW MATERIAL – ANALYTIC GEOMETRY 1. The two vertices of a triangle are A(2,4) and B(-2,3). Find the locus of the third vertex of the triangle if its area is 2 square units. a. 4x-y = 12 4y = -10 Answer:

b. 4x + 4y = 10

c. x + 4y = 12

d. x –

d

2. What are the coordinates of the center of the curve x2 + y2 -2x -4y -31 = 0? a.

(-1, -1)

Answer:

b. (-2, -2)

c. (1, 2)

d. (2, 1)

d

3. Find the eccentricity of the curve 9x2 – 4y2 -36x +8y = 4. a.

1.76

Answer:

b. 1.80

c. 1.86

d. 1.92

b

3. The slope of the line joining (2,-3) and the midpoint of the line segment joining (0,4) and (5,-2) is A.8

B.-8

C. 3

D.-3

4. Determine the equation of the line passing through (-1,3) and perpendicular to the line 4x-y +5=0. A.y - 4x - 7=0

B.x + 4y - 11=0

C.x - 4y + 13=0

D.x + 4y +11=0

5. Determine the coordinates of the centre of the circle x2-4x+y2+6y+1=0. A.(2,3)

B.(-2,3)

C. (2,-3)

D.(-2,-3)

6. If the length of the latus rectum is 3/5 of the length of minor axis, then its eccentricity is A.0.6

B.0.8

C. 1.25

D. 5/3

7. The collection of all points which is equidistant from the point (0,2) and the line y = -1 is defined by what equation? A.y2 = 6x-3.

B.x2 = 6y

C. x2 = 3-6y

D. x2 = 6y-3

8. The major axis of the elliptical path in which the Earth moves around the Sun is approximately 186,000,000 miles, and the eccentricity of the ellipse is 1/60. Determine the apogee of the Earth. Note: apogee is the point in the elliptical path farthest from the Sun. a) 91,450,000 miles

b) 93,000,000 miles c)94,335,100 miles d)94,550,000 miles

9. Find the distance of the line from (1, 5). a) 18/31

b) 18/13

c) 81/31

d) 81/13

10. What is the equation of the parabola with vertex at (0, 2) and focus at (-3, 2)? a) (y – 2)2 = 12x (x – 2)

b) (y + 2)2 = -12x

c) y 2 = 12 (x – 2)

d) y 2 = -12

11.The graph of y=(x-1)/(x+1) is asymptotic to which line? a) x = -1 only -1 and y = 1

b) x = 1 and y = 1

c) x = -1 and x = 1

d) x =

12. Determine the equation of the line a unit distance from 4x - 3y + 4=0. Let ( 0, 4/3) be a point on the given line. C = -1 -4x + 3y +1 = 0 A.

4x + 3y - 1=0

C.

-4x + 3y + 1=0

B.

B.4x + 3y + 9=0

D.

4x - 3y + 1=0

13. Compute for the eccentricity of the conic: 9x2 –16y2=144. a2 = 16 a=4

b2 = 9 b=3

e = 5/4 = 1.25 A.

0.6

c=5 C

B.0.8

C. 1.25

D. 5/3

14. Compute the y-intercept of a line passing through point (5, 3) and a slope of 3/4. a) - 3/4

b) - 5/4

c) - 3/5

d) - 4/5

15. Given the equation of the curve 9x^2+ 25y^2- 144x+200y+751=0, find the distance between its foci. a) 6 units 16. 0?

b) 8 units

c) 10 units

d) 12 units

What is the conic section described by the equation x2 + y2 – 4x + 2y – 24 = a) Circle

b) Parabola c) Hyperbola d) Ellipse

17. Find the center of the ellipse described by 4x2 + y2 – 16x – 6y –43 = 0. a) (2, 3)

b) (4, -6)

c) (1, 9)

d) (-2, -5)

18. What is the equation of the line that passes through (4, 0) and is parallel to the line x - y - 2 = 0? a) y + x - 4 = 0

b) y – x + 4 = 0

c) y – x - 4 = 0

d) y + x – 4 = 0

19. Find the area of the circle whose center is at (2, -5) and tangent to the line 4x + 3y – 8 = 0. a) 3π b) 6π c) 9π d) 12π 20. Find the eccentricity of the conic section in described by the equation x2 + y2 – 4x + 2y – 24 = 0. a) 0

b) 1

c) 1.25

d) 0.80

21. What is the x-intercept of a line passing through (1, 4) and (4, 1)? A. 4.5B. 5 C. 6 D. 4 22. The distance from point (2, 1) to the line 4x – 3y +5 = 0 is A. 2

B. 1 C. 4 D. 3

23. It is a conic section with eccentricity equals to zero. A. parabola B. circle

C. hyperbola

D. ellipse

24. What is the slope of the line joining (2,-3) and the midpoint of the line segment joining (0,4) and (5,-2)? a) 8

b)-8

c) 3

d) -3

25. Determine the coordinates of the centre of the circle x2-4x+y2+6y+1=0. a) (2,3)

b) (-2,3)

c) (2,-3)

d) (-2,-3)

26. The collection of all points which is equidistant from the point (0,2) and the line y = -1 is defined by what equation? a) y2 = 6x-3 b) x2 = 6y

c) x2 = 3-6y d) x2 = 6y-3

27. What is the conic section described by the equation 2x2 + 3y2 – 4x + 6y – 19 = 0? a) Circle

b) Parabola c) Hyperbola d) Ellipse

28. Determine B such that 3x+2y-7=0 is perpendicular to 2x-By+2=0. a) 5

b)4

c) 3

d) 2

29. The center of a circle is at (1, 1) and one point on its circumference is (-1, -3). Find the other end of the diameter through point (-1, -3). a) (2, 4)

b) (3, 5)

c) (3, 6)

d) (1, 3)

30. An ellipse with an eccentricity of 0.65 and has one of its foci 2 units from the center. The length of the latus rectum is a) 3.25 units b) 3.55 units c) 3.85 units d) 4.25 units 31. Find the standard equation of the circle passing through the points P(3, 8), Q(9, 6), and R(13, −2).