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6.b.Find the equation of the circle lies on 2x-3y+1=0 and the circle passing through the points (-1,2) and (2,3).​

Sagot :

mhanifa

Answer:

  • (x + 1)² + (y - 7)² = 25

Step-by-step explanation:

Perpendicular bisector of the chord connecting the the points (-1,2) and (2,3) is also passing through the center of the circle.

We'll find the equation of the line and solve the system to find the center.

Midpoint of the chord:

  • ((-1 + 2)/2, (2 + 3)/2) = (0.5, 2.5)

Equation of the line through chord (-1,2) and (2,3):

  • m = (3 - 2)/(2 + 1) = 1/3
  • y - 2 = 1/3(x + 1)
  • y = 1/3x + 7/3

Perpendicular bisector is:

  • y - 2.5 = -3(x - 0.5)
  • y = -3x + 4         >> (1)

And the given line is:

  • 2x - 3y + 1 = 0
  • y = 2/3x + 1/3    >> (2)

Solve the system:

  • -3x + 4 = 2/3x + 1/3
  • -9x + 12 = 2x + 1
  • 11x = -11
  • x = -1

Find y:

  • y = -3(-1) + 4 = 3 + 4 = 7

The center is (-1, 7)

Find the radius, the distance from center to one of points on circle

  • (-1, 7) and (-1, 2)
  • 7 - 2 = 5

The equation of circle is:

  • (x + 1)² + (y - 7)² = 5²
  • (x + 1)² + (y - 7)² = 25

DarlinEsteves

Hope This Helps!!!

Hope This Helps!!!Have A GREAT DAY!!!

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