Question

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

Answer 1

Answer:

• (x + 1)² + (y - 2)² = 25

Step-by-step explanation:

The center is given:

• (-1, 2)

Find the radius, the distance from the center to a point (2, 6)

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

Use circle formula:

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

Answer 2

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