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MTH103 TMA Solution 

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MTH103 List of Questions

Q1 Find the equation to the straight line passing through the point of intersection of the lines 5x+6y +1 = 0 and 3x + 2y +5 =0 and perpendicular to the line 3x-5y+11 = 0



Q2 Given that vectors P=3i+4j+5k and Q=3i+4j+5k , \[P\dot Q\] is __________



Q3 The value point A(1, -1) inside the circle is \[x^{2}+y^{2}-3x+4y=12\] ____________



Q4 Given that ellipse has equation of , the x and y intercepts of the of the equation are ______ and ______



Q5 The focus of the parabola whose equation is \[y^{2}+32\] is ________



Q6 Given that ellipse has equation of\[9x^{2}+4y^{2}=36\] , the length of the minor axis is __________



Q7 Given the equation \[9x^{2}-16y^{2}=144\], the intersection on x-axis is ___________



Q8 If a force of 30N acting in the east direction and another force of 40N acting in the north direction. Find the sum of the two vectors is _____________



Q9 The directrix of the parabola $$ y= -\frac{1}{2} x^{2}$$ is _________



Q10 The focus of the parabola $$ y= -\frac{1}{2} x^{2}$$ is _________



Q11 If A=i+4j+7k and B=5i-2j+k, find \[A\times B\]



Q12 Find the equation of the circle with centre (3, 5) and radius 3



Q13 Find the equation of the tangent at the point (0, 2) to the circle $$x^{2}+y^{2}-4x+2y-8=0$$



Q14 Find the standard form of the equation for the parabola with vertex (3, 4) with focus (5, 4).



Q15 Given the equation \[9x^2-16y^2=144\]. Find the coordinate of the foci



Q16 Given that ellipse has equation of\ 9x^2+4y^2=36\], Find the length of the major axis



Q17 Find the equation of the parabola having vertex (0, 0), axis along the x-axis and passing through (2, -10)



Q18 What is the focus in the equation \[y^2=5x\]



Q19 What is the equation of the directrix of the parabola whose equation is \[x^2-30y=0\]



Q20 Find the equation of the tangent to the circle\[ x^2+y^2-2x+4y+15=0\] at the point (-1, 2)



Q21 Find the coordinates of point of contact between the two circles \[x^2+y^2+2x+6y=39\] and \[x^2+y^2-4x-2y+1=0\]



Q22 Find the parametric equations of a circle with centre (2, -1) and radius 3



Q23 Find the points of intersection of the circle x^2+y^2-x-3y=0 with the line y=x-1.



Q24 Find the equation of the circle with circle with centre (-3, 4) which passes through the point (2, 5)



Q25 Find the equation of the circle with centre (�??2, 3) and radius 6



Q26 Find the equation of the line through the point (-1, 2) which is perpendicular to y=2x-1



Q27 Find the angle between the two lines -3x+4y=8 and -2x-8y-14=0



Q28 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



Q29 Find the sum of vectors \[\bar{AK}, \bar{KL}, \bar{LP}~~and ~~\bar{PQ}\]



Q30 A straight line has a gradient of 5/3 and it passes through the point (1,3). Find the equation of the straight line



Q31 Find the angle of slope of the line joining A(4,3) and B(9,7).



Q32 If A(3, 6) and B(4, 8) are two points on a line segment. Evaluate the coordinate of the midpoint of AB



Q33 Find the distance between the points A(4, 3) and B(6, 5)



Q34 If a=2i+4j+3k and b=i+5j-2k. Find the vector product a and b



Q35 Find the magnitude of a components of vector\[\bar{AB}=5i+2j+4k\] expressed in terms of the unit vectors



Q36 Given that\[ Z_1=2i-4j,~~Z_2=2i+6j ~~and~~ Z_3=3i-j\]. Evaluate\[ Z_1-Z_2-Z_3\]



Q37 Find the sum of vectors \[\bar{AC}+ \bar{CL}-\bar{ML}\]



Q38 Evaluate the sum of vectors \[\bar{BC}- \bar{DC}+\bar{DE}+\bar{FE}\]



Q39 Find the sum of vectors \[\bar{AK}, \bar{KL}, \bar{LP}~~and ~~\bar{PQ}\]



Q40 Find the standard equation for parabola whose directrix is the line x=2 and whose focus is the point (-2, 0)



Q41 Find the asymptotes of the hyperbola whose equation is given as \[\frac{x^{2}}{4}-\frac{y^{2}}{9}=1\]



Q42 Find equation of an ellipse whose major axis is vertical, with the center located (-1,3) at the distance between the center and one of the covertices equal to 4, and the distance between the center and one of the vertices equal to 6.



Q43 Find the equation of the parabola with focus (-1,4) and directrix y=3



Q44 Given the equation \[9x^{2}-16y^{2}=14\], Find the coordinate of the foci



Q45 Given the equation \[9x^{2}-16y^{2}=14\], Find the interception at x



Q46 Given that ellipse has an equation of \[9x^{2}+4y^{2}=36\]



Q47 Find the equation of the parabola having vertex (0,0) axis along the x-axis and pass through (2,-1)



Q48 Find the focus in the equation \[y^{2}=5x\]



Q49 Find the focus of the parabola whose equation is \[y^{2}+32x\]



Q50 Find the directrix of the parabola whose equation is \[x^{2}-30y\]



Q51 Find the equation of the circle with its center at the origin with points(-3,4) on the circle



Q52 Find the radius of a circle given by \[x=4+2\cos\theta, y=-3+2\sin\theta\]



Q53 Find the vector product \[a\times b\]. If a = i + 2j – k and b = 2i + 3j + k



Q54 Find the center of a center of a circle given by \[x=4+2\cos\theta, y=-3+2\sin\theta\]



Q55 Find the parametric equations of a circle with centre (2,-1) and radius 3



Q56 Find the point of the intersection of the center \[x^{2}+y^{2}-3y=0\] with line y=x-1



Q57 Given the equation of a circle is \[x^{2}+y^{2}+2x-6y-15\]. Find the radius of the circle



Q58 Given the equation of a circle is \[x^{2}+y^{2}+2x-6y-15\]. Find the center of the circle



Q59 Find the center of the circle \[x^{2}+y^{2}+8x + 6y = 0\].



Q60 Find the radius of the circle \[x^{2}+y^{2}+8x + 6y = 0\].



Q61 Find the equation to the straight line passing through the point of intersection of the lines 5x+6y +1 = 0 and 3x + 2y +5 =0 and perpendicular to the line 3x-5y+11 = 0



Q62 A dot product is said to be distributive,if �?â�?�¦�?â�?�¦..



Q63 If the slope of a line passing through the point A(3, 2) is \[\frac{3}{4}\]. then find points on the line which are 5 units away from the point A.



Q64 Find the equation of the line through the point (�??1, 2) which is perpendicular to y = 2x – 1



Q65 Find the equation of the line through the point (��??1, 2) which is parallel to y = 2x + 1



Q66 Find the angle between the two lines 3x+4y = 8 and 2x 8y = 14 0



Q67 A straight line has a gradient of \[\frac{5}{3}\] and it passes through the point (1,3). Find its equation



Q68 If A is (3,6) and B is (4,8). Find the coordinate of the midpoint of AB



Q69 The gradient of the line A(4,3) and B(8,6)



Q70 Find the distance between the point A(5,4) and B(7,6)



Q71 A vector having direction opposite to that of vector A,buth with the same magnitude is denoted by ———



Q72 If a=2i+4j+3k and b=i+5j-2k. Find the vector product of a and b



Q73 If a=5i+4j+2k, b=4i-5j+3k and c=2i-j-2k. Determine value \[a\dot b\]



Q74 If a= 2i+2j-k and b=3i-6j+2k. Find the scalar product a and b



Q75 Find the direction cosine [l,m,n] of the r=2i+4j-3k



Q76 If \[Z_{1}=2i-4j\],\[Z_{2}=2i+6j\] and \[Z_{3}=3i-j\] find the \[Z_{1}-Z_{2}-Z_{3}\]



Q77 If \[Z_{1}=3i+5j\] and \[Z_{2}=7i+3j\], find the \[Z_{1}-Z_{2}\]



Q78 Find the sum \[\overline{BC}-\overline{DC}+\overline{DE }+\overline{DE}+\overline{EF}\]



Q79 Find the sum \[\overline{AB}+\overline{BC}+\overline{CD}+\overline{DE}+\overline{EF}\]



Q80 If a = a force of 30N, acting in the east direction. b =a force of 40N, acting in the north direction. find the magnitude of the vector sum r of these forces



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