Browse by Stream
QnA
Home
QnA
Go To Your Study Dashboard

Get Answers to all your Questions

header-bg qa
  • Home
  • Engineering
  •  Find the value of <img alt="\lambda \text { if equation } 9 x^{2}+4 y^{2}+4 \lambda x y+4 x-2 y+3=0 \text { }" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Clambda%20%5Ctext%20%7B%2

 Find the value of \lambda \text { if equation } 9 x^{2}+4 y^{2}+4 \lambda x y+4 x-2 y+3=0 \text { }  represents a parabola

Option: 1

\lambda=\pm 6


Option: 2

\lambda=\pm 3


Option: 3

\lambda=\pm 5


Option: 4

\lambda=\pm 4


Answers (1)

best_answer

Comparing the given equation with

\\a x^{2}+b y^{2}+2 h x y+2 g x+2 f y+c=0 \\ \text {We have } a=9, b=4, c=3, h=2\lambda, g=2, f=-1

If the equation 9 x^{2}+4 y^{2}+4 \lambda x y+4 x-2 y+3=0 represents the parabola then h^2 - ab = 0

\Rightarrow (2\lambda)^{2}-(9)(4)=0 

\Rightarrow \lambda= \pm 3

Checking \Delta value for \lambda= \pm 3, \Delta comes out to be non-zero.

 

Posted by

himanshu.meshram

View full answer

Similar Questions