#### 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 (â�?�??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**