C is the center of the hyperbola (x^2)/(...

`C` is the center of the hyperbola `(x^2)/(a^2)-(y^2)/(b^2)=1` The tangent at any point `P` on this hyperbola meet the straight lines `b x-a y=0` and `b x+a y=0` at points `Qa n dR` , respectively. Then prove that `C QdotC R=a^2+b^2dot`

Similar Questions

Explore conceptually related problems

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

The tangent at the vertex of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 meets its conjugate hyperbola at the point whose coordinates are

If C is the centre of a hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 , S, S its foci and P a point on it. Prove tha SP. S'P =CP^2-a^2+b^2

Find the equation of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x_(0),y_(0)) .

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point

A point on the hyperbola x^(2)-3y^(2)=9, where the tangent is parallel to the line y+x=0, is