The equation of straight line passing through $( - a,\;0)$ and making the triangle with axes of area ‘$T$’ is
The equation of straight line passing through $( - a,\;0)$ and making the triangle with axes of area ‘$T$’ is
- A
$2Tx + {a^2}y + 2aT = 0$
- B
$2Tx - {a^2}y + 2aT = 0$
- C
$2Tx - {a^2}y - 2aT = 0$
- D
None of these
Similar Questions
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0, 0), (0, 21)$ and $(21, 0)$, is
The number of integral points (integral point means both the coordinates should be integer) exactly in the interior of the triangle with vertices $(0, 0), (0, 21)$ and $(21, 0)$, is
- [IIT 2003]
Consider the lines $L_1$ and $L_2$ defined by
$L _1: x \sqrt{2}+ y -1=0$ and $L _2: x \sqrt{2}- y +1=0$
For a fixed constant $\lambda$, let $C$ be the locus of a point $P$ such that the product of the distance of $P$ from $L_1$ and the distance of $P$ from $L_2$ is $\lambda^2$. The line $y=2 x+1$ meets $C$ at two points $R$ and $S$, where the distance between $R$ and $S$ is $\sqrt{270}$.
Let the perpendicular bisector of $RS$ meet $C$ at two distinct points $R ^{\prime}$ and $S ^{\prime}$. Let $D$ be the square of the distance between $R ^{\prime}$ and $S ^{\prime}$.
($1$) The value of $\lambda^2$ is
($2$) The value of $D$ is
Consider the lines $L_1$ and $L_2$ defined by
$L _1: x \sqrt{2}+ y -1=0$ and $L _2: x \sqrt{2}- y +1=0$
For a fixed constant $\lambda$, let $C$ be the locus of a point $P$ such that the product of the distance of $P$ from $L_1$ and the distance of $P$ from $L_2$ is $\lambda^2$. The line $y=2 x+1$ meets $C$ at two points $R$ and $S$, where the distance between $R$ and $S$ is $\sqrt{270}$.
Let the perpendicular bisector of $RS$ meet $C$ at two distinct points $R ^{\prime}$ and $S ^{\prime}$. Let $D$ be the square of the distance between $R ^{\prime}$ and $S ^{\prime}$.
($1$) The value of $\lambda^2$ is
($2$) The value of $D$ is
- [IIT 2021]
Let the area of a $\triangle PQR$ with vertices $P (5,4), Q (-2,4)$ and $R(a, b)$ be $35$ square units. If its orthocenter and centroid are $O\left(2, \frac{14}{5}\right)$ and $C(c, d)$ respectively, then $c+2 d$ is equal to :
- [JEE MAIN 2025]
Let $PS$ be the median of the triangle with vertices $P(2,\;2),\;Q(6,\; - \;1)$ and $R(7,\;3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is
Let $PS$ be the median of the triangle with vertices $P(2,\;2),\;Q(6,\; - \;1)$ and $R(7,\;3)$. The equation of the line passing through $(1, -1)$ and parallel to $PS$ is
- [IIT 2000]
If $A$ is $(2, 5)$, $B$ is $(4, -11)$ and $ C$ lies on $9x + 7y + 4 = 0$, then the locus of the centroid of the $\Delta ABC$ is a straight line parallel to the straight line is
If $A$ is $(2, 5)$, $B$ is $(4, -11)$ and $ C$ lies on $9x + 7y + 4 = 0$, then the locus of the centroid of the $\Delta ABC$ is a straight line parallel to the straight line is