The center of a circle is (h, 7) and the radius is 10. The circle passes through (3, -1). Find all possible values of h.

e q u a t i o n o f a c i rc l e : ( x − h ) 2 + ( y − 7 ) 2 = 1 0 2 i f ( x ; y ) = ( 3 ; − 1 ) , t h e n ( 3 − h ) 2 + ( − 1 − 7 ) 2 = 100 ( 3 − h ) 2 + 64 = 100 ( 3 − h ) 2 = 36 ⇔ ( 3 − h = 6 or 3 − h = − 6 ) 3 − h = 6 ⇒ h = − 3 3 − h = − 6 ⇒ h = 9 A n s . h = − 3 or h = 9

Answered by kate200468 | 2024-06-24

ce n t er o f a c i rc l e : ( a ; b ) r a d i u s : r ( x − a ) 2 + ( y − b ) 2 = r 2 ======================== ( h ; 7 ) ; r = 10 ( x − h ) 2 + ( y − 7 ) 2 = 1 0 2 ========================
T h e c i rc l e p a sses t h ro ug h t ( 3 ; − 1 ) . S u b s t i t u t e x = 3 an d y = − 1 : ( 3 − h ) 2 + ( − 1 − 7 ) 2 = 100 ( 3 − h ) 2 + ( − 8 ) 2 = 100 ( 3 − h ) 2 + 64 = 100 / − 64 ( 3 − h ) 2 = 36 ⟺ 3 − h = ± 36 ​ 3 − h = − 6 or 3 − h = 6 − h = − 6 − 3 or − h = 6 − 3 − h = − 9 or − h = 3 h = 9 or h = − 3 A n s w er : h = 9 or h = − 3

Answered by Anonymous | 2024-06-25

The possible values of h for the circle centered at (h, 7) with radius 10 that passes through the point (3, -1) are h = -3 and h = 9.
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Answered by Anonymous | 2024-10-14