Identify the curve `sqrt((x+1)^(2)+y^(2))+ sqrt(x^(2)+(y-1)^(2))-2`=0

If the locus of the moving point P(x,y) satisfying sqrt((x-1)^(2)+y^(2))+sqrt((x+1)^(2)+(y-sqrt(12))^(2))=a is an ellipse, then find the values of a.

Identify correct statement(s) about conic sqrt((x-5)^(2)+(y-7)^(2)) +sqrt((x+1)^(2)+(y+1)^(2)) =12

(dy)/(dx)=(sqrt(x^(2)-1))/(sqrt(y^(2)-1))

The tangent at a point P on the curve y =ln ((2+ sqrt(4-x ^(2)))/(2- sqrt(4-x ^(2))))-sqrt(4-x ^(2)) meets the y-axis at T, then PT^(2) equals to :

The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1 is ______

The eccentricity of the hyperbola |sqrt((x-3)^2+(y-2)^2)-sqrt((x+1)^2+(y+1)^2)|=1 is ______

An equation of the curve satisfying x dy - y dx = sqrt(x^(2)-y^(2))dx and y(1) = 0 is

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)+y^(2)))-:(sqrt(x^(2)+y^(2))+x)/(sqrt(x^(2)+y^(2))+y)

The area between the curves y=sqrt(x),y=x^(2) is

Simplify : (sqrt(x^(2)+y^(2))-y)/(x-sqrt(x^(2)-y^(2))) div (sqrt(x^(2)-y^(2))+x)/(sqrt(x^(2)+y^(2))+y)