Question

The number of straight lines which can be drawn through the point $(-2,\,\,\,2)$ so that its distance from $(-3,\,\,1)$ will be equal $6$ units is

• A. one
• B. two
• C. infinite
• D. zero

Answer 1

Answer: (D)

zero

Answer 2

Let the slope be m of the straight line which passes through
$(-2,2),$ then equation $(y-2)=m(x+2)$
$mx-y+(2m+2)=0$ ..(i)
$\because$ Perpendicular distance of line (i) from point (given) $(3,-1)=6$
$\Rightarrow$ $\frac{|m(3)-(-1)+(12m+2)|}{\sqrt{{{m}^{2}}+{{(-1)}^{2}}}}=6$
$|3m+1+2m+2|=6\sqrt{{{m}^{2}}+1}$
Squaring on both sides,
$\Rightarrow$ ${{(5m+3)}^{2}}=36({{m}^{2}}+1)$
$\Rightarrow$ $25{{m}^{2}}+9+30m=36{{m}^{2}}+36$
$\Rightarrow$ $11{{m}^{2}}-30m+27=0$ ..(ii)
Now, $\Delta ={{B}^{2}}-4AC=900-4(11)\,(27) < 0$
$\because$ Discriminate of E (ii) is negative. i.e., slope of the given line is imaginary. So, no line drawn through the point $(2,2)$ .