If `a and b` are parameters, then each line of the family of lines `x(a+2b)+y(a-3b)=a-b` passes through the point whose distance from origin is : (A) `3/5` (B) `sqrt(13)/5` (C) `sqrt(11)/5` (D) `4/5`

The distance of the point (3,4,5) from x-axis is (A) 3 (B) 5 (C) sqrt(34) (D) sqrt(41)

The distance of the point P(1,-3) from the line 2y-3x=4 is (A) 13 (B) (7)/(13)sqrt(3) (C) sqrt(13) (D) (7)/(13)

Show that the lines represented by x(a+3b)+y(2a-b)=5a+b pass through a fixed point for different values of a and b .

The distance of the point P(4,\ 3) from the origin is (a) 4 (b) 3 (c) 5 (d) 7

Prove that the line x(a+2b) + y (a-3b)=a-b passes through a fixed point for different values of a and b . Also find the fixed point.

If a ,b ,c are variables such that 3a+2b+4c=0 , then show that the family of lines givenby a x+b y+c=0 pass through a fixed point. Also, find that point.

The radius of the circle passing through the points (1, 2), (5, 2) and (5, -2) is : (A) 5sqrt(2) (B) 2sqrt(5) (C) 3sqrt(2) (D) 2sqrt(2)

If lines x+2y-1=0,a x+y+3=0, and b x-y+2=0 are concurrent, and S is the curve denoting the locus of (a , b) , then the least distance of S from the origin is (a) 5/(sqrt(57)) (b) 5/sqrt(51) (c) 5/sqrt(58) (d) 5/sqrt(59)

If the line x/a+y/b=1 passes through the points a (2,- 3) and (4, - 5), then (a, b) =

A line is perpendicular to the line 2x-3y+5=0 and passes through the points (15, beta) and (7, 17) then value of beta will be equal to (A) 35/3 (B) -35/3 (C) 5 (D) -5