#### 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

# A variable line makes intercept on the coordinate axes. If the length of perpendicular on the line from the origin is the geometric mean of the lengths of intercepts then find the locus of the foot of perpendicular draws from the origin.

3 years ago
Dear Pratham

Let the general equation of a line (L1) be of the form x/a+y/b=1 Let (h,k) lie on this line such that a normal line(L2) passing through this point intersects at the origin. Now we know that L1 is perpendicular to L2. Thus we get,

(k/h)*(-b/a)=-1

Which implies that:

k/h=a/b

Also, we know from the information provided in the question that ab=a^2+b^2, 1=a/b+b/a

From the manipulation we did above we get,

1=k/h+h/k which implies that

h^2+k^2=hk or x^2+y^2=xy.

Regards