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  • The number of lines that can be drawn through the point at a distance 12 from the point <img alt="(-2,3)" src

The number of lines that can be drawn through the point (4,-5) at a distance 12 from the point (-2,3) is

Option: 1

0


Option: 2

1


Option: 3

2


Option: 4

infinite


Answers (1)

best_answer

Let the equation of any line through (4,-5) be \mathrm{y+5=m(x-4)}

then \mathrm{\frac{3+5-m(-2-4)}{\sqrt{1+m^{2}}}= \pm 12 }

\mathrm{\Rightarrow (6 m+8)^{2}=144\left(1+m^{2}\right) }
\mathrm{\Rightarrow 27 m^{2}-24 m+20=0 }

which does not give any real value of \mathrm{m } as the discriminant \mathrm{24^{2}-80 \times 27<0 }.

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chirag

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