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  • If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154square units, then obtain the equation of the circle.

If the lines 2x – 3y = 5 and 3x – 4y = 7 are the diameters of a circle of area 154  square units, then obtain the equation of the circle.

Answers (1)

Given that the lines 2x-3y-5=0 and 3x-4y-7=0 are diameters of the circle.

2x-3y-5=0.....(i)

3x-4y-7=0....(ii)

3 (Equation (i)) - 2 (Equation (ii) ) 

 6x-9y-15-6x+8y+14=0.

y = -1

Put value of y in equation (i)

x = 1

 Solving these lines we will get the intersection as (1,-1) which is centre of the circle.

  Also, given that area of the circle is 154 sq units 

πr2=154

r2=154*7/22=49

r=7

(x-1)2+(y+1)2=49

x2+y2-2x+2y-47=0

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