Home
Class 11
MATHS
A normal to the hyperbola (x^(2))/(a^(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)`

Promotional Banner

Similar Questions

Explore conceptually related problems

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

If the normal at 'theta' on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets the transverse axis at G , and A and A' are the vertices of the hyperbola , then AC.A'G=

The line lx+my+n=0 will be a normal to the hyperbola b^(2)x^(2)-a^(2)y^(2)=a^(2)b^(2) if

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

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 to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its asymptotes at P and Q. If C its centre,prove that CP.CQ=a^(2)+b^(2)