MY CART (5)

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

ITEM
DETAILS
MRP
DISCOUNT
FINAL PRICE
Total Price: R

There are no items in this cart.
Continue Shopping
Menu
Get instant 20% OFF on Online Material.
coupon code: MOB20 | View Course list

Get extra R 280 off
USE CODE: CART20

				   

if ax^3+by^3+cx^2y+dxy^2=0 represent three distinct straight lines,such that each line bisects the angle between other two then prove that 3b+c=0

4 years ago

Share

Answers : (1)

										

Let the lines be


 


y-mix = 0 where i=1,2,3


 


As one line is equally inclined to the other two, we impose the following condition.


(m1-m3)/(1+m1m3) = -(m2-m3)/(1+m2m3)


Simplify to get,


 


(m1+m2+m3)-3m3-m3(m1m2+m2m3+m3m1)+3m1m2m3 = 0       ...........(i)


 


Similarly applying the condition on the other two pairs, we get,


 


(m1+m2+m3)-3m2-m2(m1m2+m2m3+m3m1)+3m1m2m= 0         ............(ii)


and


(m1+m2+m3)-3m1-m1(m1m2+m2m3+m3m1)+3m1m2m= 0          .......... (iii)


 


Adding equations (i),(ii) and (iii), we get,


 


-(m1m2+m2m3+m3m1)(m1+m2+m3) + 9m1m2m3 = 0                 ............(iv)


 


Putting y=mx in the equation of combined equation,


 










ax3+by3+cx2y+dxy2=0




we get,


 


bm3 + dm2 + cm + a = 0


By theory of equations,


 


m1+m2+m3 = -d/b


m1m2+m2m3+m3m1 = c/b


m1m2m3 = -a/b


 


 


Putting the above relations in equation (iv),


 


-(c/b)(-d/b) + 9(-a/b) = 0


 


cd-9ab=0


 


This is the condition that i get. No idea where i went wrong.

4 years ago

Post Your Answer

can’t we find the equation of parabola when a tangent is drawn to the parabola
 
 
We find the equation of parabola , if we know the point at which the tangent touches the parabola and the slope of the tangent.
 
SAI SANDY 5 months ago
Why does the angular bisector have to make 120 degree angle?
 
 
In this case So, bisector will make 120 (=180-60) angle with +ve x-axis
 
Akshay 10 months ago
 
In this case angle(PQR)=120. So, bisector will make 60(=120/2) angle with PQ, which is -ve x-axis. So, bisector will make 120 (=180-60) angle with +ve x-axis
 
Akshay 10 months ago
How to find the common tangent to any given curves......
 
 
Just write the equation of tangent to the curve in slope point form for both the curves..as the tangent are common equate the y intercept to get values of m... Please post any question as...
 
Sahil 6 months ago
what is integration? and what is the real life applications of an integration?
 
 
Dear Sudharshan Integration is the one symboll used in solving problems . Integration is opposite to differentiation. It is usefull in mathematics, physics and chemistry
 
Prabhakar ch 4 months ago
 
DEAR SUDARSHAN, Integration is the act of bringing together smaller components into a single system that functions as one. Integration is used to compute such things as the areas and...
 
naresh raju 4 months ago
 
dear sudarshan..... Integration is a way of adding slices to find the whole. Integration can be used to find areas, volumes, central points and many useful things. But it is easiest to...
 
mohan 4 months ago
What will will come when we differentiate acceleration
 
 
when we deferentiate the acceleration we get the jerk.
 
RAMCHANDRARAO 4 months ago
 
the rate of change of acceleration; that is, the derivative of acceleration with respect to time, and as such the second derivative of velocity, or the third derivative of position.“ it is...
 
T.kumar 4 months ago
 
MR. PRABHAKAR its nothing but “JERK“, and its a sudeen movement if u want an example then when u r travelling in the bus if driver puts a sudden brake there is movement in u i.e, jeRk
 
Dheeru chowdary 4 months ago
. Integrate tan theta- cot theta. tellllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllllll
 
 
just writre tan theta =sin theta/ costheta and let costheta as t dt = -sintheta d(theta) It becomes -dt/t = -logt = log(sectheta). Similarly you can find cot theta.
  img
Harsh Patodia 3 months ago
View all Questions »

  • Complete JEE Main/Advanced Course and Test Series
  • OFFERED PRICE: R 15,000
  • View Details
Get extra R 3,000 off
USE CODE: CART20

Get extra R 280 off
USE CODE: CART20

More Questions On Analytical Geometry

Ask Experts

Have any Question? Ask Experts

Post Question

 
 
Answer ‘n’ Earn
Attractive Gift
Vouchers
To Win!!!
Click Here for details