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If the lines 2x-3y=5 and 3x-4y=7 are the...

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.

A

`x^(2)+y^(2)+2x-2y=62`

B

`x^(2)+y^(2)+2x-2y=47`

C

`x^(2)+y^(2)-2x+2y=47`

D

`x^(2)+y^(2)-2x+2y=62`

Text Solution

Verified by Experts

The correct Answer is:
C
Since, 2x-3y = 5 and 3x-4y = 7 are diameters of a circle.
Their point of intersection is centre (1, -1)
Are given, `pir^(2) = 154`
`rArr r^(2) = 154 xx (7)/(22) rArr r = 7 `
` therefore` Required of circle is
`(x-1)^(2) + (y+1)^(2) = 7^(2)`
`rArr x^(2) + y^(2)-2x +2y = 47`
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The lines 2x-3y=5 and 3x-4y=7 are the diameters of a circle of area 154 sq.units. Then the equation of the circle is x^(2)+y^(2)+2x-2y=62x^(2)+y^(2)+2x-2y=47x^(2)+y^(2)-2x-2y=47x^(2)+y^(2)-2x+2y=62