Statement 1: The maximum value of `(sqrt(-3+4x-x^2)+4)^2+(x-5)^2(w h e r e1lt=xlt=3)i s36.` Statement 2: The maximum distance between the point `(5,-4)` and the point on the circle `(x-2)^2+y^2=1` is 6

The maximum distance of the point (4,4) from the circle x^2+y^2-2 x-15=0 is

The maximum value of x^4e^ (-x^2) is (A) e^2 (B) e^(-2) (C) 12 e^(-2) (D) 4e^(-2)

The maximum value of y = sqrt((x-3)^(2)+(x^(2)-2)^(2))-sqrt(x^(2)-(x^(2)-1)^(2)) is

The line 2x-y+1=0 is tangent to the circle at the point (2, 5) and the center of the circle lies on x-2y=4. The radius of the circle is

Statement 1 : Circles x^2+y^2=9 and (x-sqrt(5))(sqrt(2)x-3)+y(sqrt(2)y-2)=0 touch each other internally. Statement 2 : The circle described on the focal distance as diameter of the ellipse 4x^2+9y^2=36 touches the auxiliary circle x^2+y^2=9 internally.

If the maximum distance of any point on the ellipse x^2+2y^2+2x y=1 from its center is r , then r is equal to

Statement 1: The sum of coefficient in the expansion of (3^(-x//4)+3^(5x//4))^ni s2^ndot Statement 2: The sum of coefficient in the expansion of (x+y)^n i s2^ndot

Statement 1: (5x-5)^2+(5y+10)^2=(3x+4y+5)^2 is a parabola. Statement 2: If the distance of the point from a given line and from a given point (not lying on the given line) is equal, then the locus of the variable point is a parabola.

Statement 1 : If there is exactly one point on the line 3x+4y+5sqrt(5)=0 from which perpendicular tangents can be drawn to the ellipse (x^2)/(a^2)+y^2=1,(a >1), then the eccentricity of the ellipse is 1/3dot Statement 2 : For the condition given in statement 1, the given line must touch the circle x^2+y^2=a^2+1.

The equation of the cirele which passes through the point (1, 1) and touches the circle x^2+y^2+4x-6y-3=0 at the point (2, 3) on it is