A straight through a fixed point (2, 3) intersects coordinate axes at distinct points P and Q.

English

Gujarati

Hindi

9.Straight Line

hard

A straight the through a fixed point $(2, 3)$ intersects the coordinate axes at distinct points $P$ and $Q.$ If $O$ is the origin and the rectangle $OPRQ$ is completed, then the locus of $R$ is:

A

$2x + 3y = xy$

B

$3x + 2y = xy$

C

$3x + 2y = 6xy$

D

$3x + 2y = 6$.

(JEE MAIN-2018)

Solution

Equation of $PQ$ is

$\frac{x}{h} + \frac{y}{k} = 1\,\,\,\,\,\,\,……\left( 1 \right)$

Since, $(1)$ passes through the fixed point $(2,3)$ Then,

$\frac{2}{h} + \frac{3}{k} = 1\,$

Then, the locus of $R$ is $\frac{2}{x} + \frac{3}{y} = 1$ or $3x + 2y = xy$.

Standard 11

Mathematics

Share

Similar Questions

Let the points $\left(\frac{11}{2}, \alpha\right)$ lie on or inside the triangle with sides $x + y =11, x +2 y =16$ and $2 x +3 y =29$. Then the product of the smallest and the largest values of $\alpha$ is equal to :

hard

(JEE MAIN-2025)

A point starts moving from $(1, 2)$ and its projections on $x$ and $y$ – axes are moving with velocities of $3m/s$ and $2m/s$ respectively. Its locus is

hard

The line $2x + 3y = 12$ meets the $x$-axis at $A$ and $y$-axis at $B$. The line through $(5, 5)$ perpendicular to $AB$ meets the $x$- axis , $y$ axis and the $AB$ at $C,\,D$ and $E$ respectively. If $O$ is the origin of coordinates, then the area of $OCEB$ is

hard

(IIT-1976)

The equation of straight line passing through $( – a,\;0)$ and making the triangle with axes of area ‘$T$’ is

medium

The locus of a point so that sum of its distance from two given perpendicular lines is equal to $2$ unit in first quadrant, is

easy