Question

The number of points which are at a fixed non zero distance from two intersecting lines is/are

• A. 1
• B. 2
• C. 4
• D. Infinite

Answer 1

The correct option is C 4

Let Intersection point of lines is $A(x,y)$

And let the fixed distance from A of point $(a,b)$ is $1$

$\sqrt{(a-x{)}^2+(b-y{)}^2}=1$

On squaring both sides

$a^2+x^2-2ax+b^2+y^2-2by=1$

Here the above eq is quadratic hence $a$ has two values similarlly $b$ has two values

Hence the point can be 4