P`(a sec phi , a tan phi)` is a variable point on the hyperbola `x^(2) - y^(2) = a^(2)`, and A(2a,0) is a fixed point. Prove that the locus of the middle point of AP is a rectangular hyperbola.

P is a veriable poin on the hyperbola x^(2) - y^(2) =16 and A (8,0) is a fixed point . Show that the locus of the middle point of the line segment bar(AP) is another rectangular hyperbola.

P(x , y) is a variable point on the parabola y^2=4a x and Q(x+c ,y+c) is another variable point, where c is a constant. The locus of the midpoint of P Q is

Find the coordinates of the foci of the rectangular hyperbola x^(2)-y^(2) = 9

Find the equation of normal to the hyperbola 4x^(2)-9y^(2)=36 , at the point (1,2)

The normal at a point P on the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) of eccentricity e, intersects the coordinates axes at Q and R respectively. Prove that the locus of the mid-point of QR is a hyperbola of eccentricity (e )/(sqrt(e^(2)-1)) .

The locus of the middle points of the focal chords of the parabola, y^2=4x is:

Equation of a tangent to the hyperbola 5x^(2) - y^(2) = 5 and which through an external point (2, 8) is

Find the equation of the normal to the hyperbola x^(2)-y^(2)=9 at the point p(5,4).

let P be the point (1, 0) and Q be a point on the locus y^2= 8x . The locus of the midpoint of PQ is

Let P be the point (1,0) and Q be a point on the locus y^(2)=8x . The locus of the midpoint of PQ is