Find the centre and radius of the circle 2x² + 2y² - x = 0

Solution:

The equation of the given circle is 2x² + 2y² - x = 0

⇒ 2x² + 2y² - x = 0

⇒ (2x² - x) + 2y² = 0

⇒ 2 [(x²- x/2) + y²] = 0

⇒ {x² - 2 (x)(1/4) + (1/4)²} + y² - (1/4)² = 0

⇒ (x - 1/4)² + (y - 0)² = (1/4)²

which is of the form (x - h)² + (y - k))² = r²

Therefore, on comparing both equations we get

h = 1/4, k = 0 and r = 1/4

Thus, the center of the given circle is (1/4, 0) while its radius is 1/4

NCERT Solutions Class 11 Maths Chapter 11 Exercise 11.1 Question 9

Find the centre and radius of the circle 2x² + 2y² - x = 0

Summary:

The center and radius of the circle are (1/4, 0) and 1/4 respectively