Thank you for registering.

One of our academic counsellors will contact you within 1 working day.

Please check your email for login details.
MY CART (5)

Use Coupon: CART20 and get 20% off on all online Study Material

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: Rs.

There are no items in this cart.
Continue Shopping

From a point P tangents are drawn to the ellipse x^2+a^2+y^2+b^2=1.If the chord of contact touches the auxiliary circle,then the locus of P

From a point P tangents are drawn to the ellipse x^2+a^2+y^2+b^2=1.If the chord of contact touches the auxiliary circle,then the locus of P 

Grade:11

1 Answers

Saurabh Koranglekar
askIITians Faculty 10341 Points
one year ago

Let the locus of p be (h,k)So eqn. Of chord of contact to the ellipse will be xh/a^2+yk/b^2=1.Since this chord of contact is tangent to the auxillary circle,=> it`s distance from the center of the circle {I.e.(0,0)} will be the radius of the auxillary circle , I.e. `a` .Using this,|-a^2b^2|/√[(h^2)(b^4)+(k^2)(a^4)]=a=> (a^2) (b^4)=(h^2)(b^4)+(k^2)(a^4)Dividing throughout by (a^4)(b^4) and replacing h and k by x and y respectively gives us the required locus,I.e. (x^2/a^4)+(y^2/b^4)=1/(a^2)

Think You Can Provide A Better Answer ?

Provide a better Answer & Earn Cool Goodies See our forum point policy

ASK QUESTION

Get your questions answered by the expert for free