Given the circle with equation x+ y =17

Mathematics

1 answer:

barxatty [35]3 years ago

8 0

Answer:

Step-by-step explanation:

x+y=17 is NOT the equation for any circle. You have omitted the exponents. The equation for the circle should be

x^2 + y^2 = 17.

:::::

Plug the coordinates of D into the equation.

(-4)² + (-1)² = 17, so D is on the circle.

Plug the coordinates of E into the equation.

1² + 4² = 17, so E is on the circle.

:::::

Slope of DE = (-1 - 4)/(-4 - 1) = 1

Slope of perpendicular to DE is -1.

Midpoint of DE: ((-4+1)/2, (-1+4)/2) = (-1.5, 1.5)

Point-slope equation for perpendicular bisector:

y-1.5 = -(x+1.5)

y = -x

:::::

Center of circle is (0,0)

0 = -0, so y=-x passes through the center.

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