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

the equation "ax 2 +2hxy+by 2 +2gx+2fx+c=0" represents a pair of straight lines intersecting on x axis then what is the condition? ans:- 2fgh=af 2 +ch 2 please say me the way to get this answer iam thankful for those who give me answer

the equation "ax2+2hxy+by2+2gx+2fx+c=0" represents a pair of straight lines intersecting on x axis
then what is the condition?

ans:- 2fgh=af2+ch2

please say me the way to get this answer
iam thankful for those who give me answer

Grade:12th pass

1 Answers

Ashwin Muralidharan IIT Madras
290 Points
10 years ago

Hi Nikhil,

 

Let the pair of straight lines intersect at a point (p,0) on the x-axis. Hence this point must satisfy the gievn eqn.

Note that in your question, it should have been 2fy instead of 2fx.

So, ap2+0+0+2gp+0+c = 0.

Hence ap2+2gp+c = 0 is the QE, which should have co-incident roots.

Hence g2 = ac ----------(from D = 0).

 

Now for the given equation to represent a pair of St lines, the determinant

a   h   g

h   b   f

g   f   c

 

must be zero.

 

And hence a(bc-f2) - h(hc-fg) + g(hf-bg) = 0

ie abc - af2 - ch2 + 2fgh - bg2 = 0. ---------- (but g2=ac)

So 2fgh = af2+ch2 ------- (the necessary condition).

 

Hope this helps.

Wish you all the best.

 

Regards,

Ashwin (IIT Madras).

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