Home
Class 12
MATHS
P is a point on the hyperbola (x^(2))/(a...

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

A

`a^(2)`

B

`b^(2)`

C

`e^(2)`

D

`b^(2)la

Text Solution

Verified by Experts

The correct Answer is:
A
Promotional Banner

Topper's Solved these Questions

  • HYPERBOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 3|17 Videos
  • HYPERBOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise (Single Option Correct Type Questions)|30 Videos
  • HYPERBOLA

    ARIHANT MATHS ENGLISH|Exercise Exercise For Session 1|18 Videos
  • GRAPHICAL TRANSFORMATIONS

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|10 Videos
  • INDEFINITE INTEGRAL

    ARIHANT MATHS ENGLISH|Exercise Exercise (Questions Asked In Previous 13 Years Exam)|8 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

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

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).

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2, ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length 1 (b) 3 (c) 2 (d) 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

The hyperbola (x^2)/(a^2)-(y^2)/(b^2)=1 passes through the point (2,3 ) and has the eccentricity 2. Then the transverse axis of the hyperbola has the length (a)1 (b) 3 (c) 2 (d) 4

If the normal at a point P to the hyperbola meets the transverse axis at G, and the value of SG/SP is 6, then the eccentricity of the hyperbola is (where S is focus of the hyperbola)

Let P(6,3) be a point on the hyperbola parabola x^2/a^2-y^2/b^2=1 If the normal at the point intersects the x-axis at (9,0), then the eccentricity of the hyperbola is

The transverse axis of the hyperbola 5x^2-4y^2-30x-8y+121=0 is

The tangent at P on the hyperbola (x^(2))/(a^(2)) -(y^(2))/(b^(2))=1 meets one of the asymptote in Q. Then the locus of the mid-point of PQ is