1.

Compute the centre and radius of the circle 2x2 + 2y2 – x = 0​

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Answer:

SOLUTION:

Given that, the circle equation is 2x2 + 2y2 – x = 0

This can be written as:

⇒ (2x2-x) + y2 = 0

⇒ 2{[X2 – (x/2)] +y2} = 0

⇒{ x2 – 2x(¼) + (¼)2} +y2 – (¼)2 = 0

Now, simplify the above form, we get

⇒(x- (¼))2 + (y-0)2 = (¼)2

The above equation is of the form (x – h)2 + (y – k)2= r2

Therefore, by comparing the general form and the equation obtained, we can say

h= ¼ , k = 0, and R = ¼.


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