Question

Statement-1: Two real and distinct straight lines can be drawn passing through the point $M (4,-5)$ whose perpendicular distance from $P (-2,3)$ is equal to 12 .
Statement-2: Perpendicular distance of line $a x+b y+c=0$ from $\left(x_1, y_1\right)$ is $\frac{\left|a_1+b y_1+c\right|}{\sqrt{a^2+b^2}}$.

• A. Statement-1 is true, statement-2 is true and statement-2 is correct explanation for statement-1.
• B. Statement-1 is true, statement-2 is true and statement-2 is NOT the correct explanation for statement-1.
• C. Statement-1 is true, statement-2 is false.
• D. Statement-1 is false, statement-2 is true

Answer 1

Answer: (D)

If possible, let the equation of the line be $(y+5)=m(x-4)$ i.e., $y-m x+4 m+5=0$
Then $\left|\frac{3+2 m +4 m +5}{\sqrt{1+ m ^2}}\right|=12 \Rightarrow(8+6 m )^2=144\left(1+ m ^2\right) \Rightarrow 27 m ^2-24 m +20=0 \ldots$ (i)
Since discriminant of (i) is $(24)^2-4 \times 27 \times 20$, which is negative so there is no real value of $m$ which satisfies (i).
Hence no such line is possible.