Home
Class 11
MATHS
From a point G on the transerse axis of ...

From a point G on the transerse axis of the hyperbola `x^(2)/a^(2) - y^(2)/b^(2) = 1,` GL is drawn perpendicular to one of its asymptotes . Also GP is a normal to the curve at P. Prove that LP is parallel to the conjugate axis.

Promotional Banner

Similar Questions

Explore conceptually related problems

If normal to the curve x^(2)+y^(2)-2x-3=0 is parallel to the y-axis ,then :

If tangents drawn from the point (a,2) to the hyperbola (x^(2))/(16)-(y^(2))/(9)=1 are perpendicular, then the value of a^(2) is

A transvers axis cuts the same branch of a hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at P and P' and the asymptotes at Q and Q'. Prove that PQ=P'Q' and PQ'=P'Q.

Tangents at any point P is drawn to hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 intersects asymptotes at Q and R, if O is the centre of hyperbola then

The tangent at point P on the ellipse x^(2)/a^(2) + y^(2)/b^(2) = 1 cuts the minor axis in Q and PR is drawn perpendicular to the minor axis. If C is the centre of the ellipse, then CQ*CR =

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)

Find the co-ordinates of that point on the curve x^(2)/a^(2)+y^(2)/b^(2) = 1 at which the tangent drawn is parallel to Y-axis.