Home
Class 12
MATHS
if one of the diameters of the circle, g...

if one of the diameters of the circle, given by the equation, `x^(2)+y^(2)-4x+6y-12=0`, is a chord of a circles S, whose centre is at `(-3,2)` , then the radius of S is

A

`5sqrt2`

B

`5sqrt3`

C

5

D

10

Text Solution

Verified by Experts

The correct Answer is:
B
Given equation of a circle is `x^(2)+y^(2)-4x + 6y -12 =0`, whose centre is (2, - 3) and radius
`=sqrt(2^(2)+(-3)^(2)+12)=sqrt(4+9+12)=5`
Now, according to given information, we have the following figure.
`x^(2)+y^(2)-4x + 6y-12=0`
Clearly, `AO bot BC, as O` is mid-point of the chord
Now, in `DeltaAOB`, we have
`OA =sqrt((-3-2)^(2)+(2+3)^(2))`
`=sqrt(25+25)=sqrt50=5sqrt2`
`and OB = 5`
`AB=sqrt(OA^(2)+OB^(2))=sqrt(50+25)=sqrt75=5sqrt3`
Promotional Banner

Similar Questions

Explore conceptually related problems

If one of the diameters of the circle, given by the equation, x^2+y^2-4x+6y-12=0 , is a chord of a circle S, whose centre is at (-3,""2) , then the radius of S is : (1) 5sqrt(2) (2) 5sqrt(3) (3) 5 (4) 10

If one of the diameters of the circle x^2+y^2-2 x-6 y+6 =0 is a chord to the circle with centre at (2,1) then the radius of the circle is equal to.

A line 4x-3y+20=0 cuts a chord of length 8 units on a circle with centre at (-2,-1) . Find the equation of the circle.

If one end of the a diameter of the circle 2x^2+2y^2-4x-8y+2=0 is (3, 2), then find the other end of the diameter.

If one end of a diameter of a circle 2x^2 + 2y^2 - 4x - 8y + 2 = 0 is (3,2), then the other end is

Find the equation of the chord of the circle x^2+y^2=9 whose middle point is (1,-2)

Find the centre and the radius of the circle x^(2)+y^(2)+8x+10y-8=0 .

The circle whose equation is x^2 + (y - 1)^2 = 2 has the centre……………….

Find the centre and radius of circles. x^(2)+y^(2)-8x+10y-12=0 .

if x-y=3 and x+2y=6 ae the diameters of a circle then the centre is at the point………