Question

Write the standard form of the equation of the circle with the given characteristics. Center: (2, -9); Radius: square root of 17 Find the radius first! Standard form is (x-h)^2 + (y-k)^2 = r^2.

Answer 1

(x - 2)² + (y + 9)² = 17

Step-by-step explanation:

The equation of a circle in standard form is

(x - h)² + (y - k)² = r²

(h, k ) are the coordinates of the centre and r is the radius

given centre = (2, - 9 ) and r =
`√(17)` , then

(x - 2)² + (y - (-9) )² = (
`√(17)` )² , that is

(x - 2)² + (y + 9)² = 17 ← equation of circle

Answer 2

The standard form of the equation of a circle with center (2, -9) and radius √17 is (x - 2)^2 + (y + 9)^2 = 17.

Step-by-step explanation:

The question asks to write the standard form of the equation of a circle with the center at (2, -9) and a radius of the square root of 17. The standard form for the equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.

Since the center of the circle is (2, -9), h = 2 and k = -9. The radius is given as the square root of 17, so r = √17. Substituting these values into the standard form equation gives:

(x - 2)^2 + (y + 9)^2 = (√17)^2.

Finally, simplifying the radius squared term:

(x - 2)^2 + (y + 9)^2 = 17.

This is the standard form of the equation for the given circle.