If `(alpha,beta)` is a point on the circle whose center is on the x-axis and which touches the line `x+y=0` at `(2,-2),` then the greatest value of `alpha` is (a)`4-sqrt(2)` (b) 6 (c)`4+2sqrt(2)` (d) `+sqrt(2)`

If (alpha ,beta) is a point on the circle whose centre is on the x-axis and which touches the line x+y=0 at (2,-2), then the greatest value of 'alpha' is :

If C_1: x^2+y^2=(3+2sqrt(2))^2 is a circle and P A and P B are a pair of tangents on C_1, where P is any point on the director circle of C_1, then the radius of the smallest circle which touches c_1 externally and also the two tangents P A and P B is (a) 2sqrt(3)-3 (b) 2sqrt(2)-1 (c) 2sqrt(2)-1 (d) 1

If the point P(a ,a^2) lies completely inside the triangle formed by the lines x=0,y=0, and x+y=2, then find the exhaustive range of values of a is (A) (0,1) (B) (1,sqrt2) (C) (sqrt2 -1,1) (D) (sqrt2 -1,2)

The equation of a circle is x^2+y^2=4. Find the center of the smallest circle touching the circle and the line x+y=5sqrt(2)

Prove that the greatest value of x y is c^3/sqrt(2a b) , if a^2x^4+b^2y^4=c^6dot

The equation of the line that touches the curves y=x|x| and x^2+(y-2)^2=4 , where x!=0, is: (a)y=4 sqrt(5) x +20 (b)y=4 sqrt(3) x -12 (c)y=0 (d) y=-4 sqrt(5) x -20

The points on the line x=2 from which the tangents drawn to the circle x^2+y^2=16 are at right angles is (are) (a) (2,2sqrt(7)) (b) (2,2sqrt(5)) (c) (2,-2sqrt(7)) (d) (2,-2sqrt(5))

The minimum value of (x^4+y^4+z^2)/(x y z) for positive real numbers x ,y ,z is (a) sqrt(2) (b) 2sqrt(2) (c) 4sqrt(2) (d) 8sqrt(2)

The point on the parabola y^(2) = 8x at which the normal is inclined at 60^(@) to the x-axis has the co-ordinates as (a) (6,-4sqrt(3)) (b) (6,4sqrt(3)) (c) (-6,-4sqrt(3)) (d) (-6,4sqrt(3))

The coordinates of a point on the line x + y + 1 = 0 which is at a distance sqrt(2) units from the line 3x + 4y - 2 = 0 are