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)`

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 distance of the point (1, 2, 3) from the plane x+y-z=5 measured along the straight line x=y=z is 5sqrt(3) (2) 10sqrt(3) (3) 3sqrt(10) 3sqrt(5) (5) 2sqrt(5)

The shortest distance between line y-x=1 and curve x=y^2 is (a) (3sqrt2)/8 (b) 8/(3sqrt2) (c) 4/sqrt3 (d) sqrt3/4

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

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is (a) 3sqrt(5) (b) 5sqrt(3) (c) 2sqrt(5) (d) 5sqrt(2)

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

Distance between the lines 5x+3y-7=0\ a n d\ 15 x+9y+14=0 is (35)/(sqrt(34)) b. 1/(3sqrt(34)) c. (35)/(3sqrt(34)) d. 35//2sqrt(34)

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 (5sqrt(5))/8 (b) (10sqrt(5))/3 (5sqrt(5))/4 (d) none of these

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

{:(sqrt(5)x - sqrt(7)y = 0),(sqrt(7)x - sqrt(3)y = 0):}