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)`

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 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)

If P(1+t/(sqrt(2)),2+t/sqrt(2)) is any point on a line, then the range of the values of t for which the point P lies between the parallel lines x+2y=1a n d2x+4y=15. is (a) (4sqrt(2))/3lttlt5(sqrt(2)) 6 (b) 0lttlt(5sqrt(2)) (c) 4sqrt(2)lttlt0 (d) none of these

The largest value of a for which the circle x^2+y^2=a^2 falls totally in the interior of the parabola y^2=4(x+4) is (a) 4sqrt(3) (b) 4 (c) 4(sqrt(6))/7 (d) 2sqrt(3)

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)

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

If the line 3 x +4y =sqrt7 touches the ellipse 3x^2 +4y^2 = 1, then the point of contact is

If alpha,a n dbeta be t roots of the equation x^2+p x-1//2p^2=0,w h e r ep in Rdot Then the minimum value of alpha^4+beta^4 is 2sqrt(2) b. 2-sqrt(2) c. 2 d. 2+sqrt(2)

Let the length of latus rectum of an ellipse with its major axis along x-axis and center at the origin, be 8. If the distance between the foci of this ellipse is equal to the length of the minor axis , then which of the following points lies on it: (a) (4sqrt2, 2sqrt2) (b) (4sqrt3, 2sqrt2) (c) (4sqrt3, 2sqrt3) (d) (4sqrt2, 2sqrt3)