A.Maths answers on Family of St. Lines

Family of Straight Lines

Section A

1. 3 or 10/3

2. 3x+y-6=0

3. 4x+3y-12=0 or 3x+4y-12=0

4. x-3y-27=0 or 3x+y-1=0

5. 3x-4y-7=0 or 5x+12y-49=0

6. x²+y²+8y-16=0 or x²+y²-8y-16=0 

7. y=-x/3 or y=3x

8. a)  3x-2y+6+k(x+3y-1)=0 where k is a constant

    b) 11x-33y+43=0 and 33x+11y+39=0

9. a) mx-y+2-3m=0

    b) 9x - y - 25 = 0  or  5x - 3y - 9 = 0.

10.a) A is (3x/2, 0)  B is (0,3y)

    b) x²+4y²=16.  The locus is an ellipse.

11.a) 1/2 (3x+5y+1)

     b) 3x+5y-11=0   or  3x+5y+13=0.

12.5x-y-7=0  and  x+5y+9=0

13.a) F:2x+y+4+k(x-2y-3)=0 where k is a constant.

     b) x+1=0  and  3x-4y-5=0

Section B

1. a) x=u+1

    b) (u+1, (u²+2u+16)/8 )

    c) x²=8y-15

2. a) tx-4y-t²=0

    b) x-y-4=0

    c)

        |   (t-4)/(t+4)-t/4     | =1

        |1+[(t-4)/(t+4)][t/4] |

    d) prove