Home
Class 12
MATHS
Normal to a rectangular hyperbola at P m...

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

AI Generated Solution

To solve the problem, we need to find the value of \(\frac{SN}{SP}\) where \(N\) is the point where the normal to the rectangular hyperbola at point \(P\) intersects the transverse axis, and \(S\) and \(S'\) are the foci of the hyperbola. ### Step-by-Step Solution: 1. **Understanding the Hyperbola**: A rectangular hyperbola has the standard equation \(xy = c^2\). The foci of this hyperbola are located at \((\pm c\sqrt{2}, 0)\). 2. **Normal to the Hyperbola**: ...
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise SOLVED EXAMPLES|11 Videos

  • HYPERBOLA

    CENGAGE ENGLISH|Exercise CONCEPT APPLICATION EXERCISE 7.1|3 Videos

  • HIGHT AND DISTANCE

    CENGAGE ENGLISH|Exercise Archives|3 Videos

  • INDEFINITE INTEGRATION

    CENGAGE ENGLISH|Exercise Multiple Correct Answer Type|2 Videos

Similar Questions

Explore conceptually related problems

P is a point on the hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1,N is the foot of the perpendicular from P on the transverse axis. The tangent to the hyperbola at P meets the transvers axis at Tdot If O is the center of the hyperbola, then find the value of O T×O Ndot

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 tantent 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

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 tantent 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

The normal to the rectangular hyperbola xy = 4 at the point t_1 meets the curve again at the point t_2 Then

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

Find the equation of the transverse axis of the hyperbola whose foci are (4,6) and (4,-4)

If the normal to the rectangular hyperbola x^(2) - y^(2) = 4 at a point P meets the coordinates axes in Q and R and O is the centre of the hyperbola , then

If the normal at P to the rectangular hyperbola x^2-y^2=4 meets the axes at G and ga n dC is the center of the hyperbola, then (a) P G=P C (b) Pg=P C (c) P G=Pg (d) Gg=2P C

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

If the normal to the rectangular hyperbola xy = c^2 at the point 't' meets the curve again at t_1 then t^3t_1, has the value equal to