What is the center of a circle represented by the equation (x−5)2+(y+6)2=42? (−6,5) (−5,6) (5,−6) (6,−5)

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marcthemathtutor marcthemathtutor · Answer 1 · 2019-08-13T00:19:14+02:00

Answer:

(5,-6)

Step-by-step explanation:

Recall that the equation for a circle is given as:

(x – h)² + (y – k)² = r²

where, the center is represented by point (h,k) and r is the radius.

IF we compare this to our given equation:

(x−5)² + (y+6)² = 42

( x−5 )²+( y-(-6) )² = 42

we see that h = 5 and k = -6

hence the center is located at (5,-6)

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indritachandra1999 indritachandra1999 · Answer 2 · 2022-06-24T18:14:17+02:00

The center of the circle given in the question is (5 , -6).

The general equation of a circle with the center at (h , k) and radius 'r' is:

(x - h)² + (y - k)² = r²

Given equation of circle in the question:

(x - 5)² + (y + 6)² = 42

(x - 5)² + (y -(-6))² = (√42)²

Comparing this equation to the general equation:

(x - h)² + (y - k)² = r²

h = 5, k = -6

Hence, the center of the given circle is at (5 , -6)

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