The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}

Question

Nishant Vora · Answer

Hi student,
we have rectangular hyperbola
xy=c²

take a general point on this in parametric P(ct, c/t)
Now tangent at point P is T=0
xy₁ + yx₁ = 2c²
So in parametric
x(c/t) + y(ct) = 2c²
x/t + ty – 2c = 0….….…...(1)

Now centre is O(0,0)
LET foot of Perpendiculer be F(h,k)

So OF $\perp$ tangent
So product of slopes = -1
k/h * (-1/t²)= -1
hence k/h= t² ….…..(2)

Also prependicular distance OF is $\left | \frac{2c }{\sqrt{t^2 + (\frac{1}{t})^2}} \right | = \sqrt{h^2 + k^2}$

Now Put t²=k/h in above you will get the answer

I hope the solution is clear

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}

The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship

Thank you for registering.

Register Now and Win Upto 25% Scholorship for a Full Academic Year !

Enter Your Details

Registration done!

Guest

IIT JEE Courses

One Year IIT Programme

Two Year IIT Programme

Crash Course

NEET Courses

One Year NEET Programme

Two Year NEET Programme

One to One

School Board

Live Online classes

Class 11 & 12

Class 9 & 10

Class 6, 7 & 8

Test Series

JEE test series

NEET test series

C.B.S.E test series

Complete Self Study Packages

FULL COURSE

For class 12th

For class 11th

The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}

The locus of foot of perpendicular from the center of the hyperbola xy=c^2 on a variable tangent is (1){x^2-y^2}=4c^2xy (2){x^2+y^2}=2c^2xy (3){x^2+y^2}=4c^2xy (4){x^2+y^2}=4c^2xy{plese explen}

1 Answers

Think You Can Provide A Better Answer ?

Other Related Questions on Analytical Geometry

ASK QUESTION

Answer and earn gift vouchers

View courses by askIITians

Design classes One-on-One in your own way with Top IITians/Medical Professionals

Complete Self Study Package designed by Industry Leading Experts

Live 1-1 coding classes to unleash the Creator in your Child

a Complete All-in-One Study package Fully Loaded inside a Tablet!

Register Now & Win Upto 25% Scholorship