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seropon [69]
3 years ago
14

Write the standard equation of the circle if the center is (-1,2), and a point on the circle is (2,6).

Mathematics
2 answers:
ladessa [460]3 years ago
8 0

Answer:

  • (x + 1)² + (y - 2)² = 25

Step-by-step explanation:

<u>The center is given:</u>

  • (-1, 2)

<u>Find the radius, the distance from the center to a point (2, 6)</u>

  • r² = (2 - (-1))² + (6 - 2)² = 3² + 4² = 25
  • r = √25 = 5

<u>Use circle formula:</u>

  • (x - h)² + (y - k)² = r²
  • (x - (-1))² + (y - 2)² = 5²
  • (x + 1)² + (y - 2)² = 25

Juli2301 [7.4K]3 years ago
3 0

STANDARD FORM:

  • (x − h)² + (y − k)² = r², where (x, y) is any point on the circle, (h, k) is the center, and r is the radius.

ANSWER:

We are not given r, therefore, we must substitute the given point and the center into the standard form, and then compute value of r.

  • (2 − (− 1))² + (6 – 2)² = r²
  • (3)² + (4)² = r²
  • r² = 9 + 16
  • r² = 25
  • r = √25

The equation of the circle is:

  • (x − (− 1))² + (y − 2)² = (√25)²
  • (x + 1)² + (y – 2)² = 25

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