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

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

Tangents are drawn to x^(2)+y^(2)=16 from the point P(0,h). These tangents meet the x- axis at A and B. If the area of triangle PAB is minimum,then h=12sqrt(2) (b) h=6sqrt(2)h=8sqrt(2) (d) h=4sqrt(2)

The circle passing through the point (-1,0) and touching the y-axis at (0,2) also passes through the point (A) (-3/2,0) (B) (-5/2,2) (C) (-3/2,5/2) (D)(-4,0) ‘.. 2 2)

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 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

If A is the area an equilateral triangle of height h , then (a) A=sqrt(3)\ h^2 (b) sqrt(3)A=h (c) sqrt(3)A=h^2 (d) 3A=h^2

Tangents are drawn to x^2+y^2=16 from P(0,h). These tangents meet x-axis at A and B.If the area of PAB is minimum, then value of h is: (a) 12sqrt2 (b) 8sqrt2 (c) 4sqrt2 (d) sqrt2

If lines x+2y-1=0,ax+y+3=0, and bx-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)

The square root of (7+3sqrt(5))(7-3sqrt(5)) is sqrt(5)(b)2(c)4(d)3sqrt(5)

If the vertices of the hyperbola be at (-2,0) and (2,0) and one of the foci be at (-3,0) then which one of the following points does not lie on the hyperbola? (a) (-6,2sqrt(10)) (b) (2sqrt(6),5)(c)(4,sqrt(15))(d)(6,5sqrt(2))