#### 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

# Find locus of the point moving such that sum of their distances from(3,0) and(-3,0) is less than 9 units.Plz explain me the normal method as well as the other one in which we take PA+PB=2a and AB=2ae 9 years ago

Dear karhik,

the locus will be all the points INSIDE the ellipse as the definition of ellipse says that it is the locus all the points whose sum of distances from the fixed points (focii) is constant and that is equal to 2 a where coordinates of focii are (ae,0) and (-ae,0) so if the distance is less than 9

2a = 9    a=9/2

ae = 3    e = 2/3

b2 = a2 (1 - e2 )

b2 = 45/4     a2 = 81/4

ellipse is x2 /(81/4)  +  y2 /(45/4) = 1

alternate method   let the point be (h,k)    use distance formula {(h-3)2 + (k-0)2}1/2 + {(h+3)+ (k-0)2}1/2 = 9

(h-3)+ (k-0)2}1/2  = 9 - {(h+3)+ (k-0)2}1/2

now square it  twice you will get the locus of the points and after getting the final equation we get the equation

Now you can win by answering the questions on Discussion Forum. So help discuss any query on askiitians forum and become an Elite Expert League askiitian.