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Sagot :
Answer:
- x² + (y - 5)² = 10
Step-by-step explanation:
Tangent line is:
- 3y - x = 5 ⇒ 3y = x + 5 ⇒ y = 1/3 x + 5/3, the slope is 1/3
Perpendicular line to this has a slope of -3 and passes through point (1, 2).
Its equation is:
- y - 2 = -3(x - 1) ⇒ y = -3x + 3 + 2 ⇒ y = -3x + 5
Using the second line passing through the center, find the coordinates of the center:
- x + 3y = 15 ⇒ 3y = -x + 15 ⇒ y = -1/3x + 5
Solve the system by elimination:
- -3x + 5 = -1/3x + 5 ⇒ x = 0
Then
- y = 5
The center is (0, 5) and radius is the distance from center to point (1, 2):
- r² = (0 - 1)² + (5 - 2)² = 1 + 9 = 10
The equation of circle:
- (x - h)² + (y - k)² = r²
- (x - 0)² + (y - 5)² = 10 ⇒ x² + (y - 5)² = 10
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