Given the circle with equation x+ y =17 a). Determine if the points D(-4, -1) and E(1, 4) are on the circle. Show all work

b). Find the equation of the perpendicular bisector of the chord DE

c). Verify that the perpendicular bisector from part b) passes through the center of the circle

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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there are 70 more legs than eyes at the dog show (196 – 126 = 70). dogs have two more legs than eyes, and humans have the same number of legs as eyes. thus 70 is twice the number of dogs at the show, so the number of dogs is half of 70, which is 35. to get the number of humans, subtract 35 from 63: 63 – 35 = 28.

step-by-step explanation: