Maths-
General
Easy
Question
Which of the following equations describes a circle with radius 10 that passes through the origin when graphed in the xy- plane?
- (x - 5)2 + (y + 5)2 = 10
- (x - 5)2 + (y + 5)2 = 100
- (x - 10)2 + (y - 10)2 = 100
- (x - 5
)2 + (y + 5 )2 = 100
)2 + (y + 5 )2 = 100The correct answer is: (x - 5 )2 + (y + 5 )2 = 100
HINT: Try eliminating the options with the given coordinate (0, 0)
Complete step by step solution:
We know that the equation of circle is (x - h)2 (y - k)2 = r2
Given that the radius r = 10 and passes through (x, y) = (0, 0)
In option A, the RHS part must be 100 that is r2. Since it is 10, option A can be eliminated.
In option B, when (x, y) = (0, 0), we get LHS to be 50 and RHS to be 100. So option B can be eliminated.
In option C, when (x, y) = (0, 0), we get LHS to be 200 and RHS to be 100. So option C can be eliminated.
In option D, when (x, y) = (0, 0), we get LHS = 100 and RHS is given as 100.Hence option D is correct.
So, 
= 100 is the equation of a circle with radius 10 passing through the origin.
Hence option D is the correct answer.
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