The equations to the common tangents to the two hyperbolas `(x^(2))/(a^(2))-(v^(2))/(b^(2))=1 and (v^(2))/(a^(2))-(x^(2))/(b^(2))=1` are

The equation of the common tangents to the parabolas y=x^(2) and y=-(x-2)^(2) are

If e and e' are the eccentricities of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2)) =1 and (y^(2))/(b^(2))-(x^(2))/(a^(2))=1 , then the point ((1)/(e),(1)/(e')) lies on the circle:

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x^(0), y^(0)).

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

Equation of the circle passing through the intersection of ellipses (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 and (x^(2))/(b^(2))+(y^(2))/(a^(2))=1 is

The equation of the common tangent to y^(2)=2 x and x^(2)=16 y is

The condition that y=m x+c is a tangent to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2)) =1 is

The equation of the common tangent of the curves x^(2)+4y^(2)=8 and y^(2)=4x is :

The equation of the tangent to the hyperbola 4 y^(2)=x^(2)-1 at the point (1,0) is

Two conics (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 and x^(2)=-(a)/(b)y intersect, if