( `alpha,beta`) is a point on the circle whose center is on the `X` -axis and which touch 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) `4+sqrt(2)`

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, alpha) 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

The equation of the circle whose center is (3,-2) and which touches the line 3x - 4y + 13 = 0 is

The equation of the circle of radius 2sqrt(2) whose centre lies on the line x-y=0 and which touches the line x+y=4 , and whose centre is coordinate satisfy x+ygt4 , is

The value of the integral int_0^(3/2) [x^2]dx , where [] denotes the greatest integer function, is (A) 2+sqrt(2) (B) 2-sqrt(2) (C) 4+2sqrt(2) (D) 4-2sqrt(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 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 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)

A circle C_1 , of radius 2 touches both x -axis and y - axis. Another circle C_1 whose radius is greater than 2 touches circle and both the axes. Then the radius of circle is (a) 6-4sqrt(2) (b) 6+4sqrt(2) (c) 3+2sqrt(3) (d) 6+sqrt(3)

If the line y=mx+c is a tangent to the ellipse x^(2)+2y^(2)=4 , then the minimum possible value of c is (a) -sqrt(2) (b) sqrt(2) (c) 2 (d) 1