Question

3x-y+5=0 and 4x+7y+15=0 are the equation of two diameter of a circle radius 4 write down the equation of the circle​

Answer 1

Answer:

Given the equation of two diameters of a circle are 2x+y=6 and 3x+2y=4 and radius is 10 ,

we have to find equation of circle solving 2x+y=6 (1) and 3x+2y=4 ..(2)

we get to the center of circle

=> now multiple (1) by 2

we get 4x +2y = 12 ...(3)

Now subtract 2 from 3 we get

(4x+2y)−(3x+2y)=12−4

=> x=8

Putting the value of x in (1) we get

=> 2×8+y=6

=> 16+y=6

=> y=−10

Here centre of circle =(8,−10).

Equation of circle =(x−h)²+(y−k)²=r².

where (h,k) is the center of circle and r is the radius

=>(x−8)²+(y+10)²=10²

=> x²+64−16x+y²+100+20y=100

=> x²+y²−16x+20y+64=0

Hence x²+y²−16x+20y+64=0 is the required equation of circle.