If the lines represented by the equation 2x^2 | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) The general equation of a pair of straight lines passing through the origin is $ax^2 + 2hxy + by^2 = 0$. For the lines to be real,the condition is

Vedclass · Accepted Answer

$(-\infty, -4] \cup [4, \infty)$

Vedclass · Answer

(A) The general equation of a pair of straight lines passing through the origin is $ax^2 + 2hxy + by^2 = 0$. For the lines to be real,the condition is $h^2 - ab \geq 0$. Comparing $2x^2 - pxy + 2y^2 = 0$ with the general equation,we have $a = 2$,$2h = -p$ (so $h = -p/2$),and $b = 2$. Substituting these values into the condition $h^2 - ab \geq 0$: $(-p/2)^2 - (2)(2) \geq 0$ $p^2/4 - 4 \geq 0$ $p^2 - 16 \geq 0$ $(p - 4)(p + 4) \geq 0$ Solving the inequality,we get $p \leq -4$ or $p \geq 4$. Thus,$p \in (-\infty, -4] \cup [4, \infty)$.

If the lines represented by the equation $2x^2 - pxy + 2y^2 = 0$ are real,then the value of $p$ lies in the interval:

Similar Questions

If $R$ is a relation from a finite set $A$ having $m$ elements to a finite set $B$ having $n$ elements,then the number of relations from $A$ to $B$ is

The weight in grams of a non-volatile solute (mol. wt. $60$) to be dissolved in $90 \ g$ of water to produce a relative lowering of vapour pressure of $0.02$ is

In alcohol fermentation,

The structure of $Cl_2O_7$ is ......

Vedclass Test Series

Exam Paper Generator

Online Exam Module