First slide

Equation of line in Straight lines

Question

The number of lines drawn from the point (4, -5) so that its distance from (-2, 3) will be equal to 12 is

Moderate

A

2
B

1
C

4
D

None of these

Solution

$If possible, equation of line is y + 5 = m (x - 4)$
$\begin{aligned} \Rightarrow y - m x + 4 m + 5 = 0 \\ p e r p e n d i c u l a r d i s \tan c e f r o m (- 2, 3) i s \\ Then |\frac{3 + 2 m + 4 m + 5}{\sqrt{1 + m^{2}}}| = 12 \\ \Rightarrow (8 + 6 m)^{2} = 144 (1 + m^{2}) \\ \Rightarrow 27 m^{2} - 24 m + 20 = 0 \end{aligned}$
Here, discriminate < 0 Therefore, no such line possible for real value of m.

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