Question

A point is moving in such a manner that three times of distance from $x$-axis is greater by $7$ then four times of its distance from the $y$-axis, find the equation its locus.

• A. $3y-4x=7$
• B. $3y+4x=7$
• C. $3x+4y=7$
• D. None of these

Answer 1

The correct option is A $3y-4x=7$

Let $P(x,y)$ be any position of the moving point on its locus.

Then the distance of $P$ from the $x$-axis is $y$ and its distance from the $y$-axis is $x$.

Since it is given that three times of distance from $x$-axis is greater by $7$ then four times of its distance from the $y$-axis,

Hence, $3y–4x=7$ is the required equation to the locus of the moving point.