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JEE Main 2010
Exam
JEE Main
Year
2010
Subject
Mathematics
Chapter
Circle

JEE Main 2010 · Mathematics · Circle

The circle x^2+y^2=4 x+8 y+5 intersects the line 3 x-4 y=m at two...

The circle x2+y2=4x+8y+5x^2+y^2=4 x+8 y+5 intersects the line 3x−4y=m3 x-4 y=m at two distinct points if

Options

  1. A−35<m<15-35 < m < 15
  2. B15<m<6515 < m < 65
  3. C35<m<8535 < m < 85
  4. D−85<m<−35-85 < m < -35

Correct answer

A. −35<m<15-35 < m < 15

Step-by-step solution

Circle x2+y2−4x−8y−5=0x^2+y^2-4 x-8 y-5=0 Centre =(2,4)=(2,4), Radius =4+16+5=5=\sqrt{4+16+5}=5 If circle is intersecting line 3x−4y=m3 x-4 y=m at two distinct points. ⇒\Rightarrow length of perpendicular from centre << radius ⇒∣6−16−m∣5<5\Rightarrow \frac{|6-16-\mathrm{m}|}{5} < 5 ⇒∣10+m∣<25\Rightarrow|10+\mathrm{m}| < 25 ⇒−25<m+10<25\Rightarrow-25 < m+10 < 25 ⇒−35<m<15\Rightarrow-35 < \mathrm{m} < 15.
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