Tangents are drawn from points on a tangent of the hyperbola `x^(2) - y^(2) = a^(2)` to the hyperbola `y^(2) = 4ax`. If all the chords of contact pass through Q, the locus of point Q for different tangents on the hyperbola is a/an

Tangents are drawn from the points on a tangent of the hyperbola x^2-y^2=a^2 to the parabola y^2=4a xdot If all the chords of contact pass through a fixed point Q , prove that the locus of the point Q for different tangents on the hyperbola is an ellipse.

Tangents are drawn from any point on the hyperbola (x^2)/9-(y^2)/4=1 to the circle x^2+y^2=9 . Find the locus of the midpoint of the chord of contact.

The locus of the mid-point of the chords of the hyperbola x^(2)-y^(2)=4 , that touches the parabola y^(2)=8x is

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

A tangent to the hyperbola x^(2)/4 - y^(2)/1 = 1 meets ellipse x^(2) + 4y^(2) = 4 in two distinct points . Then the locus of midpoint of this chord is

Equation ofa tangent passing through (2, 8) to the hyperbola 5x^(2) - y^(2) = 5 is

If x= 9 is a chord of contact of the hyperbola x^(2) -y^(2) =9 , then the equation of the tangents at one of the points of contact is

Tangents drawn from a point on the circle x^2+y^2=9 to the hyperbola x^2/25-y^2/16=1, then tangents are at angle

The tangent at a point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (0,-b) and the normal at P passes through the point (2asqrt(2),0) . Then the eccentricity of the hyperbola is

Tangents are drawn to a hyperbola from a point on one of the branches of its conjugate hyperbola. Show that their chord of contact will touch the other branch of the conjugate hyperbola.