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 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)

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

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

If the normal at P(theta) on the hyperbola (x^2)/(a^2)-(y^2)/(2a^2)=1 meets the transvers axis at G , then prove that A GdotA^(prime)G=a^2(e^4sec^2theta-1) , where Aa n dA ' are the vertices of the hyperbola.

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

If the normal at a pont P to the hyperbola x^2/a^2 - y^2/b^2 =1 meets the x-axis at G , show that the SG = eSP.S being the focus of the hyperbola.

For hyperbola x^2/a^2-y^2/b^2=1 , let n be the number of points on the plane through which perpendicular tangents are drawn.

A normal to the hyperbola, 4x^2_9y^2 = 36 meets the co-ordinate axes x and y at A and B. respectively. If the parallelogram OABP (O being the origin) is formed, then the locus of P is :-

If the line lx+my+n=0 touches the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 . Then

A normal to the hyperbola x^2-4y^2=4 meets the x and y axes at A and B. The locus of the point of intersection of the straight lines drawn through A and B perpendicular to the x and y-axes respectively is