Let R be the interior region between the line | vedclass

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

Question

(B) Let $P = (a^2, a+1)$.For line $L_1: 3x-y+1=0$,the origin $(0,0)$ gives $L_1(0,0) = 3(0)-0+1 = 1 > 0$.Since $P$ lies on the same side as the origin

Vedclass · Accepted Answer

$(-3,0) \cup (\frac{1}{3}, 1)$

Vedclass · Answer

(B) Let $P = (a^2, a+1)$.For line $L_1: 3x-y+1=0$,the origin $(0,0)$ gives $L_1(0,0) = 3(0)-0+1 = 1 > 0$.Since $P$ lies on the same side as the origin,$L_1(a^2, a+1) > 0$.$3(a^2) - (a+1) + 1 > 0$ $\Rightarrow 3a^2 - a > 0$ $\Rightarrow a(3a-1) > 0$.Thus,$a \in (-\infty, 0) \cup (\frac{1}{3}, \infty) \dots (i)$.For line $L_2: x+2y-5=0$,the origin $(0,0)$ gives $L_2(0,0) = 0+2(0)-5 = -5 Since $P$ lies on the same side as the origin,$L_2(a^2, a+1) $a^2 + 2(a+1) - 5 Thus,$a \in (-3, 1) \dots (ii)$.Taking the intersection of $(i)$ and $(ii)$:$a \in (-3, 0) \cup (\frac{1}{3}, 1)$.

Let $R$ be the interior region between the lines $3x-y+1=0$ and $x+2y-5=0$ containing the origin. The set of all values of $a$,for which the points $(a^2, a+1)$ lie in $R$,is :

Similar Questions

$O(0,0), B(-3,-1), C(-1,-3)$ are vertices of a triangle $OBC$. $D$ is a point on $OC$ and $E$ is a point on $OB$. If the equation of $DE$ is $2x + 2y + \sqrt{2} = 0$,then the ratio in which the line $DE$ divides the altitude of the triangle $OBC$ from $O$ to $BC$ is:

If a line $l$ passes through $(k, 2k), (3k, 3k)$ and $(3, 1)$,where $k \neq 0$,then the distance from the origin to the line $l$ is

$A$ straight line makes equal negative intercepts on the coordinate axes. If the perpendicular distance from the origin to the line is $4 \text{ units}$, then the equation of the line is:

$A$ straight line passes through the points $(5,0)$ and $(0,3)$. The length of the perpendicular from the point $(4,4)$ to the line is:

If $x + 2y = 3$ is a line and $A(-1, 3)$,$B(2, -3)$,and $C(4, 9)$ are three points,then:

Vedclass Test Series

Exam Paper Generator

Online Exam Module