Suggestion for HSC exam 2013

12 Jun

COORDINATES

  1. Find a  if the distances of the point  (a,5)  from the y-axis and the point (7, 2) are equal .   [C.B.2007; J.B. 2006; R.B.2004; S.B.2003 ]
  2. Find the ratio in which the -x-axis divides the straight line joining the points  and  find the abscissa of the point of division.      [S.B. 2007; R.B.2006, 2003; C.B.2005;c.B.2004; D.B.2002]
  3. Coordinates of the extremities of a diagonal of a parallelogram are (3,  and  If the third vertex is find the coordinate of the fourth vertex of the parallelogram .     [D.b. 2007 ;C.B.2006, 2004; S.B.2003; C.B.2000]
  4. Coordinates of the vertices of a triangle are  Find the area of the triangle and show that when  or,  the points will be collinear.        [B.B 2007; S.B. 2007; D.B.2006; C.B.2003; C.B.2001]
  5. Coordinates of the vertices of a triangle are  and  If the centric of the triangle is on the -axis , show that     [C.B.2006; S.B.2005; D.b.2003,2001; B.B.2001]

THE STRAIGHT LINE

  1. If  and  cos  sin  represent the same straight line , express  in terms of and    [R.B.2007; D.B.2004; J.B.2003; S.B.2002 ]
  2. A straight  line passes through the point and intersects the  and -axes at the points A and  B respectively such that OA +2. OB = 0 where O is the origin. Find its equation.    [S.B.2007; D.B.2006,2001 J.B. 2006; C.B.206; R.B.2004 ]
  3. Find the coordinates of the middle point of the intercept of the straight line  between the axes. If this intercept be the side of a square, find its area.    [D.B.2007,2001 J.B. 2007; B.B.2005; S.B. 2003; R.B. 2003; C.B.2001 ]
  4.  is a point on the straight line  and   is a point on the straight line  Find the equation of AB.    [R.B. 2007,2005,2001; B.B. 2004,2001; C.B. 2004,2000; D.B. 2002,2000; C.B.2002 ]
  5. Find the equation of the perpendicular bisector of the straight line joining the points    [D.B.2006; C.B.2006; B.B.2004,2003; R.B.2003]
  6. The straight lines  and  are at equal distances from the origin. Find the positive value of  c.   [C.B. 2006,2004; J.B.2005; B.B.2004; R.B. 2000]
  7. Show that the point (0 ,1) lies on one of the bisectors of the angle between the straight lines  and    [R.B.2006,2001; D.B.2005,2002; S.B.2004; C.B.2003]

CIRCLE

  1. A circle passes through the origin and cuts off intercepts  3 and  5 from the positive direction of the  and -axes respectively. Find the equation of the circle.   [S.B. 2007,2002; D.B.2006, 20032001; R.B.2006, 2001; C.B.2005,2001; B.B.2004 ]
  2. Find the equation of the circle whose centre is at the point  (4, 5) and which passes through the centre of the circle    [D.B.2007,2001; C.B.2006,2004,2002; C.B.2006,2004;S.B. 2005;B.B. 2005; R.B.2004, 2001; J.B.2000 ]
  3. A circle has its centre at the point  (1, 2) and it touches the -axis. Find its equation and the length of the intercept which it cuts off from the -axis.        [R.B.2007,2001 ; B.B.2007 ; C.B.2005; S.B. 2003 ; J.B.2002 ;D.B.2000 ]
  4. The circle  touches the -axis. Find  c and the coordinates of the point of contact.        [D.B. 2007, 2004, 2003; S.B. 2007; R.B. 2005; J.B. 2005 ; C.B.2005 ]
  5. The chord of the circle  is bisected at the point  ( . Find the equation of the chord.     [D.B. 2007,2003 ; R.B. 2006, 2003 ; C.B.2006, 2001 ; C.B.2006, 2004; S.B. 2005,2003 ; J.B. 2003 ;B.B.2002 ]
  6. Find the equation of the parabola whose focus is the point  (1, 1) and the equation of whose directory is Find also the equation of its axis    [ D.B. 2007,2001 ; R.B. 2005,2000 ; C.B.2005,2002 ; Ch.B. 2005; B.B. 2005,2001; J.B.2002 ]
  7. Find the equation of the hyperbola whose focus is the point , eccentricity is  and the equation of the directrix  is     [ S.B. 2007, 2004 ; D. B. 2006 ; C.B.2006,2003 ; J.B. 2006, 2002 ; Ch.B.2006, 2004 ; R.B. 2005 ; B.B. 2005, 2003 ]

VECTOR

  1. Show that the diagonals of parallelogram bisect each other       [D.B.2007,2005 ; R.B.2007,2005, 2002 ; C.B.2007, 2005, 2003 ; J.B. 2007, 2002 ; Ch.B. 2006 ; S.B.2003 ; B.B. 2003 ]
  2. Prove that in any triangle ABC,

(i)                  cos        [J.B. 2007, 2003 ; C.B.2007 ; D.B. 2006,2001; B.B.2005 ; S.B.2004 ;R.B.2003 ]

  1. Find  so that the three vectors  and   may be coplanar.    [C.B. 2006 ; Ch. B. 2006 ; B.B. 2006 ; D.B.2004 ; S.B. 2003 ]
  2. If    = 3  +2    and  =    find the unit vector parallel to the resultant of the vectors  and .
  3. Find the component of the vector        along the vector       .   [D.B. 2007; C.B. 2006,2002 B.B. 2006; J.B. 2005;S.B. 2004 ]
About these ads

Leave a Reply

Fill in your details below or click an icon to log in:

WordPress.com Logo

You are commenting using your WordPress.com account. Log Out / Change )

Twitter picture

You are commenting using your Twitter account. Log Out / Change )

Facebook photo

You are commenting using your Facebook account. Log Out / Change )

Google+ photo

You are commenting using your Google+ account. Log Out / Change )

Connecting to %s

Follow

Get every new post delivered to your Inbox.

%d bloggers like this: