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 line x-y+2=0 touches the parabola y^2 = 8x at the point (A) (2, -4) (B) (1, 2sqrt(2)) (C) (4, -4 sqrt(2) (D) (2, 4)

The radius of circle which passes through the focus of parabola x^(2)=4y and touches it at point (6,9) is k sqrt(10), then k=

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)

The radius of the circle, which touches the parabola y^2 = 4x at (1,2) and passes through the origin is:

Let C be the circle with centre (1,1) and radius 1. If T is the circle centered at (0,k) passing through origin and touching the circle C externally then the radius of T is equal to (a) (sqrt(3))/(sqrt(2)) (b) (sqrt(3))/(2) (c) (1)/(2) (d) (1)/(4)

Let C be the circle with centre at (1, 1) and radius = 1. If T is the circle centred at (0, y), passing through origin and touching the circle C externally, then the radius of T is equal to (1) (sqrt(3))/(sqrt(2)) (2) (sqrt(3))/2 (3) 1/2 (3) 1/4

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)

A circle passes through the points A(1,0) and B(5,0), and touches the y-axis at C(0,h). If /_ACB is maximum,then (a)h=3sqrt(5)(b)h=2sqrt(5)(c)h=sqrt(5)(d)h=2sqrt(10)

The radius of a circle,having minimum area, which touches the curve y=4-x^(2) and the lines,y=|x| is: (a) 4(sqrt(2)+1)( b) 2(sqrt(2)+1) (c) 2(sqrt(2)-1)( d) 4(sqrt(2)-1)

If x=((sqrt(5)-2))/(sqrt(5)+2) and y=(sqrt(5)+2)/(sqrt(5)-2) find (i)