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liraira [26]
3 years ago
8

Consider a circle centered at C(0,0). If the point P(3,5) lies on the circle, then which of the following points also lies on th

e circle?
A. (-2,6)
B. (6,-\sqrt{5})
C. (1,\sqrt{33})
D. (-2\sqrt{2},4)
Mathematics
1 answer:
Zarrin [17]3 years ago
8 0

Answer:

C

Step-by-step explanation:

First find the equation of the circle

the general formula for a circle (x-h)² + (y-k)² = r² where (h=0, k=0) are the coordinates of the center and r is the radius that we do not know

the distance between the center (0, 0) and the point (3,5) is the radius

distance formula d² = (x2-x1)² +(y2-y1)²  where (x1=0,y1=0) and (x2=3, y2=5)

d² = (3-0)² + (5-0)² = 3² +5² = 9+ 25 = 34 =r²

(x-0)² + (y-0)² = 34 ; x²+y² =34 is the equation of the circle

Second check if any of the points are on the circle by substituting x and y with de given coordinates.

A. for (-2, 6) we have (-2)²+6² =34 so 4+36 =34 false

B. for (6, -√5) we have 6²+(-√5)² =34 so 36+5=34 false

C. for (1, √33) we have 1²+(√33)² =34 so 1+33 =34 true

D. for (-2√2, 4) we have (-2√2)²+4² =34 so 8+16=34 false

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Please check the attached graph.

From the diagram, it is clear that Lizbeth is 5.5 ft tall, seeing the top from 318 feet away, making an angle of elevation to be 72⁰.

The diagram makes a right-angled triangle.

  • Given the angle = Ф = 72⁰
  • Adjacent = a = 5.5 ft
  • Opposite = b = 318 ft
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Pythagorean Theorem:

For a right-angled triangle, with sides 'a' and 'b', the hypotenuse 'c' is defined as:

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c=\sqrt{5.5^2+318^2}

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