Chords of the circle `x^(2)+y^(2)=4`, touch the hyperbola `(x^(2))/(4)-(y^(2))/(16)=1`.The locus of their middle-points is the curve `(x^(2)+y^(2))^(2)=lambdax^(2)-16y^(2)`, then the value of `lambda` is

Chords of the hyperbola, x^2-y^2 = a^2 touch the parabola, y^2 = 4ax . Prove that the locus of their middlepoints is the curve, y^2 (x-a)=x^3 .

From the points on the circle x^(2)+y^(2)=a^(2) , tangents are drawn to the hyperbola x^(2)-y^(2)=a^(2) : prove that the locus of the middle-points (x^(2)-y^(2))^(2)=a^(2)(x^(2)+y^(2))

If the line y=3x+lambda touches the hyperbola 9x^(2)-5y^(2)=45 , then the value of lambda is

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

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

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

There are two perpendicular lines, one touches to the circle x^(2) + y^(2) = r_(1)^(2) and other touches to the circle x^(2) + y^(2) = r_(2)^(2) if the locus of the point of intersection of these tangents is x^(2) + y^(2) = 9 , then the value of r_(1)^(2) + r_(2)^(2) is.

The locus of middle points of normal chords of the rectangular hyperbola x^(2)-y^(2)=a^(2) is

The locus of the middle points of chords of the circle x^(2)+y^(2)=25 which are parallel to the line x-2y+3=0 , is

The mid point of the chord x+2y+3=0 of the hyperbola x^(2)-y^(2)=4 is