Find the points on the curve `5x^2-8x y+5y^2=4` whose distance from the origin is maximum or minimum.

Find the coordinates of a point the parabola y^(2)=8x whose distance from the focus is 10.

Find the points on y -axis whose perpendicular distance from the line 4x-3y-12=0 is 3.

Find the maximum distance of any point on the curve x^2+2y^2+2x y=1 from the origin.

Find the points on the curve y^(2)-4xy=x^(2)+5 for which the tangent is horizontal.

Find the points on the line x + y = 1 that lie at a distance 3 units from the line 5x+12y = 3.

The coordinates of a point on the parabola y^2=8x whose distance from the circle x^2+(y+6)^2=1 is minimum is (2,4) (b) (2,-4) (18 ,-12) (d) (8,8)

The coordinates of a point on the parabola y^2=8x whose distance from the circle x^2+(y+6)^2=1 is minimum is (a) (2,4) (b) (2,-4) (c) (18 ,-12) (d) (8,8)

Find the points on the curve y^(2) - 4xy = x^(2) + 5 for which the tangent is horizontal.