#### Thank you for registering.

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

Click to Chat

1800-5470-145

+91 7353221155

CART 0

• 0
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

# P  is a variable point on the line y=4.Tangents PA and PB are drawn to the circle x2+y2=4. A point Q is taken such that parallelogram PAQB is completed.Prove that locus of Q is(y+4)(x2+y2)=2y2 .

2 years ago
Dear Ishaan

chord of contact of circle from P is

ax +4y =4 .............1

equation of chord bisected at a point O is

x(a+h)/2  + y (k+4)/2 -4 = {(a+h)/2}2  + {(k+4)/2} -4

x(a+h)/2  + y (k+4)/2  = {(a+h)/2}2  + {(k+4)/2}  ....................2

equation 1 and 2 represent same line AB so

(a+h)/2a   = (k+4)/2*4    =  [{(a+h)/2}2  + {(k+4)/2}2  ]/4

so  (a+h)/2a   = (k+4)/2*4

1+ h/a  = k/4 +1

a = 4h/k

and   (k+4)/2*4    =  [{(a+h)/2}2  + {(k+4)/2}2  ]/4

( k+4)/2    =    {(4h/k+h)/2}2  + {(k+4)/2}2

( k+4)/2    =    {(4h/k+h)/2}2  + {(k+4)/2}2

( k+4)/2    =   h2/k2 {(k+4)/2}2  + {(k+4)/2}

(k+4)(h² +k²)=2k²