A pair of straight lines drawn through the origin form with the line $2x + 3y = 6$ an isosceles right angled triangle, then the lines and the area of the triangle thus formed is
A pair of straight lines drawn through the origin form with the line $2x + 3y = 6$ an isosceles right angled triangle, then the lines and the area of the triangle thus formed is
- A
$x - 5y = 0$ ; $5x + y = 0$ ; $\Delta = \frac{{36}}{{13}}$
- B
$3x - y = 0$ ; $5x + y = 0$ ; $x + 3y = 0$; ;$\Delta = \frac{{36}}{{13}}$$\Delta = \frac{{12}}{{17}}$
- C
$5x - y = 0$ ; $x + 5y = 0$ ; $\Delta = \frac{{13}}{5}$
- D
None of these
Similar Questions
The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. unit. The locus of the point is
The point moves such that the area of the triangle formed by it with the points $(1, 5)$ and $(3, -7)$ is $21$ sq. unit. The locus of the point is
Let the line $x+y=1$ meet the axes of $x$ and $y$ at $A$ and $B$, respectively. A right angled triangle $A M N$ is inscribed in the triangle $O A B$, where $O$ is the origin and the points $M$ and $N$ lie on the lines $OB$ and $A B$, respectively. If the area of the triangle AMN is $\frac{4}{9}$ of the area of the triangle $OAB$ and $AN : NB =\lambda: 1$, then the sum of all possible value$(s)$ of is $\lambda$ :
- [JEE MAIN 2025]
If $P = (1, 0) ; Q = (-1, 0) \,\,ane\,\, R = (2, 0)$ are three given points, then the locus of the points $S$ satisfying the relation, $SQ^2 + SR^2 = 2 SP^2$ is :
If $P = (1, 0) ; Q = (-1, 0) \,\,ane\,\, R = (2, 0)$ are three given points, then the locus of the points $S$ satisfying the relation, $SQ^2 + SR^2 = 2 SP^2$ is :
Let $A B C$ be an isosceles triangle in which $A$ is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$ is on the positive $\mathrm{x}$-axis. If $\mathrm{BC}=4 \sqrt{3}$ and the line $\mathrm{BC}$ intersects the line $y=x+3$ at $(\alpha, \beta)$, then $\frac{\beta^4}{\alpha^2}$ is :
Let $A B C$ be an isosceles triangle in which $A$ is at $(-1,0), \angle A=\frac{2 \pi}{3}, A B=A C$ and $B$ is on the positive $\mathrm{x}$-axis. If $\mathrm{BC}=4 \sqrt{3}$ and the line $\mathrm{BC}$ intersects the line $y=x+3$ at $(\alpha, \beta)$, then $\frac{\beta^4}{\alpha^2}$ is :
- [JEE MAIN 2024]
A square of side a lies above the $x$ -axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha ,(0 < \alpha < \frac{\pi }{4})$ with the positive direction of $x$-axis. The equation of its diagonal not passing through the origin is
A square of side a lies above the $x$ -axis and has one vertex at the origin. The side passing through the origin makes an angle $\alpha ,(0 < \alpha < \frac{\pi }{4})$ with the positive direction of $x$-axis. The equation of its diagonal not passing through the origin is
- [AIEEE 2003]