Let P b any point on the hyperbola`(x^(2))/(a^(2))-(y^(2))/(b^(2))=1` whose ordinate is PN. AA′ is its transverse axis. If the point Q divides AP in the ratio `a^(2):b^(2)`, then NQ is?

P N is the ordinate of any point P on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 and A ' is its transvers axis. If Q divides A P in the ratio a^2: b^2, then prove that N Q is perpendicular to A^(prime)Pdot

The slope of the tangent to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( x_(1),y_(1)) is-

The slop of the normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point ( a sec theta , b tan theta) is -

Let P(4,3) be a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 . If the normal at P intersects the x-axis at (16,0), then the eccentriclty of the hyperbola is

P is a point on the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 , and N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transverse axis at T. If O is the centre of the hyperbola, then OT.ON is equal to

Let the eccentricity of the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 be reciprocal to that of the ellipse x^(2)+9y^(2)=9 , then the ratio a^(2):b^(2) equals

Let P(a sec theta , b tan theta ) and Q(a sec phi , b tan phi) where theta + phi = (pi)/(2) be two point on the hyperbola (x^(2))/(a^(2)) - (y^(2))/(b^(2)) =1 .If ( h, k) be the point of intersection of the normals at P and Q , then the value of k is -

Find the equations of the tangent and normal to the hyperbola (x^(2))/(a^(2))-(y^(2))/(b^(2))=1 at the point (x0, y0).

If the tangent at any point on the ellipse (x^(2))/(a^(2)) + (y^(2))/(b^(2)) =1 intersects the coordinate axes at P and Q , then the minimum value of the area (in square unit ) of the triangle OPQ is (O being the origin )-

Let P be a point on the circle x^(2) + y^(2) = a^(2) whose ordinate is PN and Q is a point on PN such that PN : QN = 2 : 1 . Find the locus of Q and identify it