A normal to the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` meets the axes at `Ma n dN` and lines `M P` and `N P` are drawn perpendicular to the axes meeting at `Pdot` Prove that the locus of `P` is the hyperbola `a^2x^2-b^2y^2=(a^2+b^2)dot`

A normal to the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 meets the axes at Ma n dN and lines M P and N P are drawn perpendicular to the axes meeting at Pdot Prove that the locus of P is the hyperbola a^2x^2-b^2y^2=(a^2+b^2)^2 dot

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)

A normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the axes in M and N and lines MP and NP are drawn perpendicular to the axes meeting at P. Prove that the locus of P is the hyperbola a^(2)x^(2)-b^(2)y^(2)=(a^(2)+b^(2))^(2)

A normal to the hyperbola x^(2)//a^(2) -y^(2)//b^(2) =1 cuts the axes at K and L. The perpendicular at K and L to axes meet in P. The locus of P is

A normal to (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes in L and M . The perpendiculars to the axes through L and M intersect at P .Then the equation to the locus of P is

Ifthe normal at P the rectangular hyperbola x^(2)-y^(2)=4 meets the axes in G and g and C is the centre of the hyperbola,then

A tangent (x^(2))/(a^(2))+(y^(2))/(b^(2))=1 meets the axes at A and B.Then the locus of mid point of AB is