The point, at shortest distance from the line `x+y=10` and lying on the ellipse `x^2+2y^2=6,` has coordinates (A) `(sqrt2,sqrt2)` (B) `(0,sqrt3)` (C) `(2,1)` (D) `(sqrt5, 1/sqrt2)`

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)

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)

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 locus of a point that is equidistant from the lines x+y-2sqrt2=0 and x+y-sqrt2=0 is

The shortest distance from the point (1,2,-1) to the surface of the sphere x^(2)+y^(2)+z^(2)=54 is a) 3sqrt(6) b) 2sqrt(6) c) sqrt(6) d)2

The shortest distance between the line yx=1 and the curve x=y^(2) is (A)(3sqrt(2))/(8) (B) (2sqrt(3))/(8) (C) (3sqrt(2))/(5) (D) (sqrt(3))/(4)

The shortest distance form the point (1,2,-1) to the surface of the sphere (x+1)^(2)+(y+2)^(2)+(z-1)^(2)=6 (A) 3sqrt(6) (B) 2sqrt(6) (C) sqrt(6) (D) 2

The shortest distance form the point (1,2,-1) to the surface of the sphere (x+1)^(2)+(y+2)^(2)+(z-1)^(2)=6 (A) 3sqrt(6) (B) 2sqrt(6) (C) sqrt(6) (D) 2

The eccentricity of the ellipse 4x^(2)+9y^(2)=36 is (1)/(2sqrt(3)) b.(1)/(sqrt(3)) c.(sqrt(5))/(3) d.(sqrt(5))/(6)

Distance of origin from the line (1+sqrt3)y+(1-sqrt3)x=10 along the line y=sqrt3x+k (1) 2/sqrt5 (2) 5sqrt2+k (3) 10 (4) 5