MTH 103 Question and Answers

Q1. Evaluate the sum of vectors \[\bar{BC}- \bar{DC}+\bar{DE}+\bar{FE}\] 
\[\bar{BF}\]  
\[\bar{BE}\] 
 \[\bar{BD}\] 
 \[\bar{DB}\] 

Q2. Find the equation of the circle with circle with centre (-3, 4) which passes through the point (2, 5)  
\[x^{2}+y^{2}+6x-8y=1\]  
\[x^{2}+y^{2}+2x+3y-12=0\]  
\[x^2+y^2+3x-2y-5=0\]  
\[x^2+y^2+3x-5y-6=0\] 

Q3. Find the coordinates of point of contact between the two circles \[x^2+y^2+2x+6y=39\] and \[x^2+y^2-4x-2y+1=0\]  
\[(3\frac{1}{5}, 2\frac{3}{5})\] 
 \[(3\frac{3}{5}, 4\frac{1}{5})\] 
 \[(2\frac{4}{5}, 4\frac{2}{5})\]  
\[(5\frac{2}{5}, 3\frac{1}{5})\]

 Q4. Find the sum of vectors \[\bar{AK}, \bar{KL}, \bar{LP}~~and ~~\bar{PQ}\]  
\[\bar{AQ}\] 
 \[\bar{AP}\] 
 \[\bar{AK}\]  
\[\bar{KP}\] 

Q5. A straight line has a gradient of 5/3 and it passes through the point (1,3). Find the equation of the straight line  
3y=5x-8  
2y=6x-2  
y=2x-4  
6y=x-3

Q6. A straight line has a gradient of 5/3 and it passes through the point (1,3). Find the intercept of the straight line on the y-axis  
-8/3  
-7/5  
-3/4 
 -3/4 

Q7. Find the equation of the line through the point (�??1, 2) which is perpendicular to y = 2x - 1
  \[\frac{-1}{2}x+\frac{3}{2}\] 
 \[\frac{1}{2}x-\frac{3}{4}\]  
\[\frac{3}{7}x+\frac{1}{2}\] 
 \[\frac{3}{2}x+\frac{1}{2}\]

 Q8. Find the parametric equations of a circle with centre (2, -1) and radius 3  
\[x=2+3 \cos\theta,~~ y=-1+3 \sin⁡\theta\]  
\[x=-1+3 \cos\theta,~~ y=2+3 \sin⁡\theta\] 
 \[x=4+9\cos\theta,~~ y=1+9 \sin⁡\theta\] 
 \[x=1+9 \cos\theta,~~ y=4+9\sin⁡\theta\] 

Q9. Find the equation of the circle with centre (�??2, 3) and radius 6  
\[x^{2}+y^{2}+4x-6y=23\]  
\[x^{2}+y^{2}+26x-y=3\]  
\[x^{2}+y^{2}+3x-2y=5\]  
\[x^{2}+y^{2}+25x-23y=10\] 

Q10. Find the angle between the two lines -3x+4y=8 and -2x-8y-14=0 
 \[-14.63^{0}\]  
\[-15.45^{0}\]  
\[-12.37^{0}\] 
 \[-24.63^{0}\]