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

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 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

The straight lines joining any point P on the parabola y^(2)=4ax to the vertex and perpendicular from the focus to the tangent at P intersect at R. Then the equation of the locus of R is x^(2)+2y^(2)-ax=02x^(2)+y^(2)-2ax=02x^(2)+2y^(2)-ay=0(d)2x^(2)+y^(2)-2ay=0

If normal at any point P to the ellipse (x^(2))/(a^(2))+(y^(2))/(b^(2))=1(a>b) meets the axes at A and B such that PA:PB=1:2, then the equation of the director circle of the ellipse is

The tangent at any point to the circle x^(2)+y^(2)=r^(2) meets the coordinate axes at A and B.If the lines drawn parallel to axes through A and B meet at P then locus of P is

A line L_(1) : (x)/(10)+(y)/(8)=1 intersects the coordinate axes at points A and B . Another line L_(2) perpendicular to L_(1) intersects the coordinate axes at C and D . The locus of circumcentre of Delta ABD is

Two perpendicular tangents to the circle x^(2)+y^(2)=a^(2) meet at P. Then the locus of P has the equation