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 radius of circle touching parabola y^(2)=x at (1,1) and having directrix of y^(2)=x as its normal is

Let the radius of the circle touching the parabola y^(2)=x at (1, 1) and having the directrix of y^(2)=x at (1, 1) and having the directrix of y^(2)=x as its normal is equal to ksqrt5 units, then k is equal to

If y=2x+3 is a tangent to the parabola y^(2)=24x, then is distance from the parallel normal is 5sqrt(5)(b)10sqrt(5)(c)15sqrt(5)(d) None of these

Radius of the circle that passes through the origin and touches the parabola y^(2)=4ax 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

P is a point on the line y+2x=1, and Q and R two points on the line 3y+6x=6 such that triangle PQR is an equilateral triangle.The length of the side of the triangle is (2)/(sqrt(5)) (b) (3)/(sqrt(5))(c)(4)/(sqrt(5))(d) none of these

Length of the latus rectum of parabola with focus (3,-4) and directrix 6x-7y+5=0 will be (A) (51)/(sqrt(85)) (B) (102)/(sqrt(85)) (C) (204)/(sqrt(85)) (D) none of these

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 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)

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 3sqrt(5)(b)5sqrt(3)(c)2sqrt(5)(d)5sqrt(2)

The eccentricity of the ellipse 4x^(2)+9y^(2)=36 is (1)/(2sqrt(3)) b.(1)/(sqrt(3)) c.(sqrt(5))/(3) d.(sqrt(5))/(6)