If a circle with center at the origin passes through the point (0,5),

Question

If a circle with center at the origin passes through the point (0,5), through which of the following points does it also pass?

(A) (2, √21) 
(B) (4, 5) 
(C) (5, √21)
(D) (5, 5) 
(E) (5, 12)

exc4libur · Accepted Answer

Given: a circle centered at the origin is equal to coordinates (0,0) and the circle that passes through the point (0,5) has a radius equal to 5.
Question: find the choice that has the same distance as the radius of the circle = 5.

To calculate the distance between the origin and a point:  \sqrt{(x^2+y^2)}

Note: most choices contain a 5 and anything with a square root greater than 25 is larger than 5, so eliminate all choices that contain 5 = BCDE.

(A) (2, √21) =  \sqrt{(2^2+√21^2)} = √25 = 5  this is the correct choice.

(B) (4, 5) = √(16+25) > 5
(C) (5, √21) = √(25+21) > 5
(D) (5, 5) = √(25+25) > 5
(E) (5, 12) = √(25+144) > 5

karthikkaushik91 · Answer

The answer is A I suppose, coz the distance from origin to (0,5) is 5 so any option that satisfies the distance as 5 could be the answer. All suggestions accepted if I m wrong in good humour  
Cheers,
Karthik

Sent from my iPhone using GMAT Club Forum

GMATBusters · Answer

circle with center at the origin passes through the point (0,5) , this means radius = 5.
we need to find another point which is at a distance of radius(5) from centre (0,0).
Only option A satisfies this...
Distance of (2, root 21) from (0,0) = (4+21)^0.5 = 5.

Hence Answer is A

generis · Answer

The basic equation of a circle yields the answer quickly.

A circle with  center at origin * has the basic equation (Pythagorean theorem, where r = h):
 x^2 + y^2 = r^2

Radius, r = 5. From (0,5) and (0,0): (5-0) = 5

This circle's equation is
 x^2 + y^2 = 5^2 
 x^2 + y^2 = 25

Any two points on the circle must satisfy the equation: Square each coordinate. They must now sum to 25.

Eliminate answers B, C, D, and E

All have 5 as one coordinate. 5^2 = 25 
The other coordinate would have to be 0 for the Pythagorean theorem to hold.

By POE, the answer is A (2, √21) 
And   (2^2 + √21^2) = (4 + 21) = 25

In case there is doubt:
 x^2 + y^2 = 25

(B) (4, 5)
  (4^2 + 5^2) = (16 + 25) = 41  
(C) (5, √21)
  (5^2 + √21^2) = (25 + 21) = 46  
(D) (5, 5)
  (5^2 + 5^2) = (25 + 25) = 50  
(E) (5, 12)
  (5^2 + 12^2) = (25 + 144) = 169

Answer A

*If the circle is not centered at origin, that is, has center (h,k), the general equation for a circle is used
 (x - h)^2 + (y - k)^2 = r^2

Subhrajyoti · Answer

If the radius is 5 then the circle will cut at 5 on x axis as well, why are we computing distance . I am not sure i understand this logic

PrafulLata · Answer

The Equation of circle whose radius "r" unit and has its center at the origin is 
x^2 + y^2 = r^2

Here, r is 5 
So  simplified equation  would be: x^2 + y^2 = 25
  Condition  : The sum of square of value of x and y must be 25
and only option A satisfies the condition.

Therefore   Option A   is correct answer

bumpbot · Answer

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If a circle with center at the origin passes through the point (0,5),

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