A `(-2,0)` and B(2, 0) are two fixed points and P is a point such that `PA-PB=2`. Let S be the circle `x^(2)+y^(2)=r^(2)`. Then match the following lists:

Match the following lists:

Let the foci of the hyperbola `(X^(2))/(A^(2))-(y^(2))/(B^(2))=1` be the vertices of the ellipse `(x^(2))/(a^(2))+(y^(2))/(b^(2))=1` and the foci of the ellipse be the vertices of the hyperbola. Let the eccentricities of the ellipse and hyperbola be `e_(E)` and `e_(H)`, respectively. Then match the following lists.

If the ellipse `x^(2)+k^(2)y^(2)=k^(2)a^(2)` is confocal with the hyperbola `x^(2)-y^(2)=a^(2)`, then match the following lists and choose the correct code.

Match the following lists:

Let`H:(x^(2))/(a^(2))-(y^(2))/(b^(2))=1`, where a gt b gt 0, be a hperbola in the xy-plane whose conjugate axis LM subtends and angle of `60^(@)` at one of its vertices N. Let the area of the triangle LMN be `4sqrt3`.

The correct option is :

Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively.

If a tangent to a suitable conic (List I) is fond to be y = x+8 and its point of contact is (8, 16), then which of the following options I sthe only CORRECT combination?

Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively.

For `a=sqrt2` if a tangent is drawn to a suitable conic (List I) at the point of contact `(-1,1)`, which of the following options is the only CORRECT combination for obtaining its equation?

Match the conic in List I with the statements/expressions in List II.

Lists I, II and III contains conics, equation of tangents to the conics and points of contact, respectively.

If the tangent to a suitable conic (List I) at `(sqrt3(1)/(2))` is found to be `sqrt3x+2y=4`. then which of the following options is the only CORRECT combination?