Question

The equation of the circle with (1,1) as centre and which cuts a chord of length 4$\sqrt 2$units on the line x+y+1=0 is

Answer 1

Answer:

○《1.1》×=10 y=29

Step-by-step explanation:

10×29 = 290÷10○=29=[0.322]

Answer 2

Given :  the circle with (1,1) as centre and which cuts a chord of length 4units on the line x+y+1=0 is

To find : The equation of the circle

Solution:

Let say Equation of circle

(x - 1)² + (y - 1)² = r² as center is (1 , 1) and radius is unknown

cuts a chord of length 4√2units on the line x+y+1=0

Perpendicular Distance of ( 1, 1) center from    line x+y+1=0

Distance of point (x₁ , y₁) from Ax + By + C = 0

is given by  |  (Ax₁ + By₁ + C) / √(A² + B²) |

Hence

=  | (1 (1)  + 1(1)  + 1 ) /( √(1²  + 1²)) |

=  3 / √2

Half chord length = 2√2    perpendicular from center bisect chord

using Pythagoras theorem

radius²  = ( 2√2)²  + (3/√2)²

=> r²  =  8  + 9/2

=> r²  =  25/2

(x - 1)² + (y - 1)² = 25/2

(x - 1)² + (y - 1)² = 25/2  is the   equation of the circle

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