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JEE Main 2006
Exam
JEE Main
Year
2006
Subject
Mathematics
Chapter
Circle

JEE Main 2006 · Mathematics · Circle

If the lines 3 x-4 y-7=0 and 2 x-3 y-5=0 are two diameters of a...

If the lines 3x−4y−7=03 x-4 y-7=0 and 2x−3y−5=02 x-3 y-5=0 are two diameters of a circle of area 49π49 \pi square units, the equation of the circle is

Options

  1. Ax2+y2+2x−2y−47=0x^2+y^2+2 x-2 y-47=0
  2. Bx2+y2+2x−2y−62=0x^2+y^2+2 x-2 y-62=0
  3. Cx2+y2−2x+2y−62=0x^2+y^2-2 x+2 y-62=0
  4. Dx2+y2−2x+2y−47=0x^2+y^2-2 x+2 y-47=0

Correct answer

D. x2+y2−2x+2y−47=0x^2+y^2-2 x+2 y-47=0

Step-by-step solution

Point of intersection of 3x−4y−7=03 x-4 y-7=0 and 2x−3y−5=02 x-3 y-5=0 is (1,−1)(1,-1), which is the centre of the circle and radius =7=7. ∴\therefore Equation is (x−1)2+(y+1)2=49⇒x2+y2−2x+2y−47=0(x-1)^2+(y+1)^2=49 \Rightarrow x^2+y^2-2 x+2 y-47=0
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