For which of the following curves, the line `x + sqrt3 y = 2sqrt3` is the tangent at the point `((3sqrt3)/(2), 1/2)` ?

x+sqrt3.y=2sqrt3 is tangent to a curve at ((3sqrt3)/2 ,1/2) then curve can be

Which of the following points lies on the tangent to the curve x^4 e^y + 2 sqrt(y + 1) = 3 at the point (1, 0 )?

To which of the circles,the line y-x+3=0 is normal at the point (3+3sqrt(2),3sqrt(2)) is

The graph of straight line y = sqrt(3)x + 2sqrt(3) is :

If x = 2 +sqrt3, y = 2 - sqrt3 then the value (x^2+y^2)/(x^3+y^3) is

The coordinates (2,3) and (1,5) are the foci of an ellipse which passes through the origin. Then the equation of the (a)tangent at the origin is (3sqrt(2)-5)x+(1-2sqrt(2))y=0 (b) tangent at the origin is (3sqrt(2)+5)x+(1+2sqrt(2)y)=0 (c)tangent at the origin is (3sqrt(2)+5)x-(2sqrt(2+1))y=0 (d) tangent at the origin is (3sqrt(2)-5)-y(1-2sqrt(2))=0

Find the angle which the line joining the points (1, sqrt3) and (sqrt2, sqrt6) makes with the x-axis.

The point at which the tangent to the curve y=sqrt(4x-3)-10 has slope (2)/(3) is