Home
Class 12
MATHS
The lines 2x-3y=5 and 3x-4y=7 are the di...

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 (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`

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`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the equation of tangent to the circle x^(2) + y^(2) + 2x -3y -8 = 0 at (2,3)

Find the equations to the common tangents of the circles x^2+y^2-2x-6y+9=0 and x^2+y^2+6x-2y+1=0

The line x+3y=0 is a diameter of the circle x^2+y^2-6x+2y=0

The line 2x+3y=5 , 2x+y=k , 2x-y-1=0

The equation of a circle of radius 1 touching the circles x^2+y^2-2|x|=0 is (a) x^2+y^2+2sqrt(2)x+1=0 (b) x^2+y^2-2sqrt(3)y+2=0 (c) x^2+y^2+2sqrt(3)y+2=0 (d) x^2+y^2-2sqrt(2)+1=0

Find the image of the circle x^2+y^2-2x+4y-4=0 in the line 2x-3y+5=0

Find the angle at which the circles x^2+y^2+x+y=0 and x^2+y^2+x-y=0 intersect.

From the points (3, 4), chords are drawn to the circle x^2+y^2-4x=0 . The locus of the midpoints of the chords is (a) x^2+y^2-5x-4y+6=0 (b) x^2+y^2+5x-4y+6=0 (c) x^2+y^2-5x+4y+6=0 (d) x^2+y^2-5x-4y-6=0

If points Aa n dB are (1, 0) and (0, 1), respectively, and point C is on the circle x^2+y^2=1 , then the locus of the orthocentre of triangle A B C is (a) x^2+y^2=4 (b) x^2+y^2-x-y=0 (c) x^2+y^2-2x-2y+1=0 (d) x^2+y^2+2x-2y+1=0

Find the equation of the normal to the circle x^2+y^2-2x=0 parallel to the line x+2y=3.