Normal to a rectangular hyperbola at P meets the transverse axis at N. If foci of hyperbola are S and S', then find the value of `(SN)/(SP).`
Text Solution
Verified by Experts
We know that PN is angle bisector of focal radii SP and S'P. `therefore" "(SP)/(S'P)=(SN)/(S'N)` `therefore" "(SN)/(SP)=(S'N)/(S'P)=|(SN-S'N)/(SP-S'P)|=(SS')/(|SP-S'P|)=e=sqrt2`
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
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
P Q and R S are two perpendicular chords of the rectangular hyperbola x y=c^2dot If C is the center of the rectangular hyperbola, then find the value of product of the slopes of C P ,C Q ,C R , and C Sdot
The length of the transverse axis of the hyperbola 9y^(2) - 4x^(2) = 36 is -
If the latus rectum and the transverse axis of a hyperbola are equal, show that it is a rectangular hyperbola.
The chord P Q of the rectangular hyperbola x y=a^2 meets the axis of x at A ; C is the midpoint of P Q ; and O is the origin. Then A C O is (a) equilateral (b) isosceles (c) right-angled (d) right isosceles
If S_1a n dS_2 are the foci of the hyperbola whose length of the transverse axis is 4 and that of the conjugate axis is 6, and S_3a n dS_4 are the foci of the conjugate hyperbola, then the area of quadrilateral S_1S_3S_2S_4 is 24 (b) 26 (c) 22 (d) none of these
If asymptotes of hyperbola bisect the angles between the transverse axis and conjugate axis of hyperbola, then what is eccentricity of hyperbola?
Show that the normal to the rectangular hyperbola xy=c^(2) at point t meet the curve again at t' such that t^(3)t'=1 .
The slope of the normal to the rectangular hyperbola xy=4 "at" (2t, (2)/(t)) is -
