A square is inscribed in the circle x 2 + y 2 − 10 x − 6 y + 30 = 0 . One side of this square is parallel to y = x + 3 . If ( x i , y i ) are the vertices of the square, then Σ ( x i 2 + y i 2

Question

A square is inscribed in the circle x 2 + y 2 − 10 x − 6 y + 30 = 0 . One side of this square is parallel to y = x + 3 . If ( x i ​ , y i ​ ) are the vertices of the square, then Σ ( x i 2 ​ + y i 2 ​ ) is equal to:

TestHub · Accepted Answer

y = x + c & y = x + c & ​ 2 ​ 5 − 3 + c ​ ​ = 2 ​ ∣ c + 2∣ = 2 c = 0 , − 4 ​ x + y + d = 0 ​ 2 ​ 8 + d ​ ​ = 2 ​ 8 + d = ± 2 d = − 10 , − 6 ​ pts ( 5 , 5 ) , ( 3 , 3 ) , ( 7 , 3 ) , ( 5 , 1 ) ​ ∑ ( x i 2 ​ + y 1 2 ​ ) = 25 + 25 + 9 + 9 + 49 + 9 + 25 + 1 = 152 ​

Mathematics - Circle Question with Solution | TestHub

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