1. A variable straight line, drawn through the point of intersection of the straight lines  x/a + y/b = 1  and      

x/b + y/a = 1  meets the coordinate axes in A and B.

Show that the locus of mid point of AB is the curve

2(a + b)xy = ab(x + y).

2. If sum of the distances of a point from two perpendicular lines  in a plane is 1, then its locus is

a) square                   b)circle

c)straight line             d)two intersecting lines

3. The line ( p + 2q)x + (p-3q)y = p-q for different values  of p and q passes through rhe point

a) (3/2 , 5/2)                 b) (2/3  , 2/5)

c) (3/5 , 3/5)                 d) (2/5 , 3/5 )

4. If x/c + x/d = 1 be any line through the intersection of lines x/a + x/b = 1 and x/b + x/a = 1, then

a) 1/a + 1/d = 1/b + 1/c                     b) 1/b + 1/d = 1/c + 1/a

c) 1/c + 1/d = 1/a + 1/b                     d)n.o.t

5.  The eqn. to the pair of straight lines through the origin and perpendicular

to 2 - 4xy - 7 = 0 is ...................................?

6. If a + 2hxy + b + 2gx + 2fy + c = 0 represents a pair of lines, equidistant from the origin, then

a) = c( bf - ag )                          b) - = c( b - a )

c)  + = c( b + a )             d) n.o.t

7. The eqn. of bisector of that angle b/w the lines x + y + 1 = 0   and

2x - 3y - 5 =0 which contains the point ( 10 , -20 ) is ..............................?

8. A point moves so that sum of squares of its distances from the four sides of a  square  is constant. This point lies on a

a) straight line                                       b) circle

c) ellipse                                               d) parabola

9. Given the system of straight lines a( 2x + y - 3 ) + b( 3x + 2y - 5 ) = 0, the

line of the system situated farthest from the point ( 4, -3 ) has the eqn.  ................................?

10. If point (4 , 5 ) is rotated by anticlockwise though the origin the new point is ..............................?

11. All points lying inside the triangle formed by the points ( 1,3 ) , ( 5 , 0 ) and ( -1 , 2 ) satisfy

a) 3x + 2y 0                                 b) 2x + y - 13 0

c) 2x - 3y - 12 0                           d) -2x + y 0

12. The line L  has intercepts  a and b on the co-ordinate axes. When keeping the origin fixed, the co-ordinate axes are rotated through a fixed angle, then the same line has intercepts p and q on the rotated axes, then

a) + = +                           b) + = +

c) + = +                          d) + =  +  

13. The area of triangle is 5sq. units and two of its vertices are(2 ,1 ) and 

( 3 , -2 ). The third vertex which lies on yhe line y = x + 3 is

a) (-3/2,3/2) correct                                                                b) (5/2,11/2)

c) (7/2.13/2) correct                                      d) (0,0)

14. If one of the diag0nals of a square is along the line x = 2y and one of its vertices is (3,0), then the eqns. of the sides through this vertex are given

by ...........................?

15. The eqn. h + ( 1- )xy  - h = 0 represents a pair of straight lines, then

a) h =2 necessarily                                   b) h = -2  necessarily

c) h may be any real number                    d) n.o.t

for  d 5th q

d ansewr is 7x^2+4xy-2y^2=0

c if ther's ne combined equation of straigth lines ax^2-2hxy+by^2=0.....which passes thru d origin then d equation of line perpendicular 2 it is given by bx^2+2hxy+ay^2=0

yeh raata mar lo.......wat u hav 2 do is just change d sign of d middle term and change d coefficients of d other two...

note .this is only and only if they pass thru origin

for the 15th question..............................

                                                       if they should reperesnt a pair of lines then they shud satisfy....

                                            h square greater than ab......caluculate tat and u find is satisfies for all real values of h

for 13th the answer is c draw the traingle and find the length of its base....then height to caluculate the area will be perpendicular distance from the third vertex to the line u have got.....so multiply 1/2 base*height and u will get it

and for 12th one though rotate it,,...perpendicular distance remains the same.....so its answer is c

For 13th question,take the third vertex as (x , x+3) and substitute in the area of triangle formula

[y = x+3 is given]..on solving |4x-4| = 10 will be obtained

4x-4 = 10                                                                        4x-4 = -10

x = 7/2                                                                              x = -3/2 

substitute x=7/2 in y=x+3                                          substitute x= -3/2 in y= x+3

y = 13/2                                                                        y = 3/2

3rd vertex is ( 7/2,13/2)                                                3rd vertex is (-3/2,3/2)  

The questions 1,3,4,5,13,15 are already answered.Let me answer some of the remaining questions.

2)Let us assume the lines to be X,Y axes for convenience.Then,P(x₀,y₀) belongs to the locus iff Ix₀I+Iy₀I=1.Thus the locus is a square formed by the lines IxI+IyI=1 with centre as origin.

8)Let us assume the square to be formed by the lines x=0,y=0,x=a,y=a.Then the sum of squares of distances of a point (x,y) from the four sides is

x²+y²+(x-a)²+(y-a)²=k,a constant.

2x²+2y²-2ax-2ay+2a²-k=0. which is a circle for ka².

10)When rotated thro' an angle k,the point (x,y) becomes (x',y')

where x'=xcosk+ysink and y'=-xsink+ycosk.

Here,k=pi/4 and (x,y)=(4,5) and so,(x',y')=(9/rt2,1/rt2).