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 lines 2x + y - 3 = 0 , 5x + ky - 3 = 0 " and " 3x - y - 2 = 0 are concurrent , find the value of k.

If the lines 3x + 4y+ 1 = 0, 5x +lambda y + 3 = 0 and 2x + y-1 = 0 are concurrent, then lambda=

Radius of the circle that passes through the origin and touches the parabola y^2=4a x at the point (a ,2a) is (a) 5/(sqrt(2))a (b) 2sqrt(2)a (c) sqrt(5/2)a (d) 3/(sqrt(2))a

The equation of the lines passing through the point (1,0) and at a distance (sqrt(3))/2 from the origin is (a) sqrt(3)x+y-sqrt(3) =0 (b) x+sqrt(3)y-sqrt(3)=0 (c) sqrt(3)x-y-sqrt(3)=0 (d) x-sqrt(3)y-sqrt(3)=0

The radius of the circle touching the parabola y^2=x at (1, 1) and having the directrix of y^2=x as its normal is (a)(5sqrt(5))/8 (b) (10sqrt(5))/3 (c)(5sqrt(5))/4 (d) none of these

The length of the chord of the parabola y^2=x which is bisected at the point (2, 1) is (a) 2sqrt(3) (b) 4sqrt(3) (c) 3sqrt(2) (d) 2sqrt(5)

Tangent of acute angle between the curves y=|x^2-1| and y=sqrt(7-x^2) at their points of intersection is (5sqrt(3))/2 (b) (3sqrt(5))/2 (5sqrt(3))/4 (d) (3sqrt(5))/4

In A B C , the coordinates of the vertex A are (4,-1) , and lines x-y-1=0 and 2x-y=3 are the internal bisectors of angles Ba n dC . Then, the radius of the encircle of triangle A B C is 4/(sqrt(5)) (b) 3/(sqrt(5)) (c) 6/(sqrt(5)) (d) 7/(sqrt(5))

Solve sqrt(5)x^(2) + x + sqrt(5)=0

The straight lines x+2y-9=0,3x+5y-5=0 , and a x+b y-1=0 are concurrent, if the straight line 35 x-22 y+1=0 passes through the point (a) (a , b) (b) (b ,a) (c) (-a ,-b) (d) none of these