NIMCET 2013 — Mathematics PYQ

1. Identify the relationship between the lines:

Line 1: $3x-4y+4=0$

Line 2: $6x-8y-7=0$

Divide Line 2 by $2$ to make the coefficients of $x$ and $y$ identical to Line 1:

Since the coefficients of $x$ and $y$ are proportional, the lines are parallel. Parallel tangents to a circle always lie on opposite sides, meaning the distance between them is the diameter of the circle.

2. Calculate the distance between parallel lines ($d$):

The distance $d$ between two parallel lines $Ax+By+C_1=0$ and $Ax+By+C_2=0$ is:

Here, $A=3$, $B=-4$, $C_1=4$, and $C_2=-3.5$ (or $-\frac{7}{2}$):

3. Find the radius ($r$):

Since the distance between the parallel tangents is the diameter: