The distance between the parallel lnes `y=2x+4 and 6x-3y-5` is (A) `1` (B) `17/sqrt(3)` (C) `7sqrt(5)/15` (D) `3sqrt(5)/15`

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

The radius of the circle touching the straight lines x-2y-1=0 and 3x-6y+7=0 is (A) 1/sqrt(2) (B) sqrt(5)/3 (C) sqrt(3) (D) sqrt(5)

Shortest distance between two parabolas y^(2)=x-2 and x^(2)=y-2 is :( A) (1)/(4sqrt(2))(B)(5)/(4sqrt(2))(C)(7)/(2sqrt(2))(D)(6)/(7sqrt(2))

The angle between the straight lines x -y sqrt3=5 and sqrt3x +y =7 is

The line L given by (x)/(5)+(y)/(b)=1 passes through the point (13,32). The line K is parallel to L and by has the equation (x)/(c)+(y)/(3)=1. Then the distance between L and K is (a) sqrt(17)quad (b) (17)/(sqrt(15)) (c) (23)/(sqrt(17)) (d) (23)/(sqrt(15))

The equaiton of the line which bisects the obtuse angle between the lines x-2y+4=0 and 4x-3y+2=0 (A) (4-sqrt(5))x-(3-2(sqrt(5)) y+ (2-4sqrt(5))=0 (B) (3-2sqrt(5)) x- (4-sqrt(5))y+ (2+4(sqrt(5))=0 (C) (4+sqrt(5)x-(3+2(sqrt(5))y+ (2+4(sqrt(5))=0 (D) none of these

The angle between the lines y = (2-sqrt(3))X + 5 and y = (2+sqrt(3))X - 7 is

The length of the tangent of the curve y=x^(2)+2 at (1, 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)

The length of the tangent of the curve y=x^(2)+2 at (1 3) is (A) sqrt(5) (B) 3sqrt(5) (C) 3/2 (D) (3sqrt(5))/(2)