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If the point (x, 4) lies on a circle whose center is at the origin and radius is 5, What is the value of x?
- a)±4
- b)0
- c)±3
- d)±5
Correct answer is option 'C'. Can you explain this answer?
Most Upvoted Answer
If the point (x, 4) lies on a circle whose center is at the origin and...
The distance between the point (x, 4) and the origin (0, 0) is equal to the radius of the circle, which is 5.
Using the distance formula, we have:
√((x - 0)^2 + (4 - 0)^2) = 5
Simplifying this equation, we have:
√(x^2 + 16) = 5
Squaring both sides of the equation, we have:
x^2 + 16 = 25
Subtracting 16 from both sides of the equation, we have:
x^2 = 9
Taking the square root of both sides of the equation, we have:
x = ±3
Therefore, the possible values of x are 3 and -3.
Using the distance formula, we have:
√((x - 0)^2 + (4 - 0)^2) = 5
Simplifying this equation, we have:
√(x^2 + 16) = 5
Squaring both sides of the equation, we have:
x^2 + 16 = 25
Subtracting 16 from both sides of the equation, we have:
x^2 = 9
Taking the square root of both sides of the equation, we have:
x = ±3
Therefore, the possible values of x are 3 and -3.
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Community Answer
If the point (x, 4) lies on a circle whose center is at the origin and...
OP = 5
⇒ OP2 = 25
⇒ (x - 0)2 + (4 - 0)2 = 25
⇒ x2 + 16 = 25
⇒ x2 = 9 ⇒ x = ± 3
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