Question

The intercept on the line y = x by the circle x² + y² - 2x = 0 is AB. The equation of the circle with AB as diameter is ______.

विकल्प

• x² + y² + x + y = 0

• x² + y² - x - y = 0

• x² + y² - 3x + y = 0

• x² + y² + 3x - y = 0

Answer 1

The intercept on the line y = x by the circle x² + y² - 2x = 0 is AB. The equation of the circle with AB as diameter is x² + y² - x - y = 0.

Explanation:

We have equation of line y = x and equation of circle x² + y² - 2x = 0

Now, intersecting points of given line and circle,

x² + x² - 2x = 0

⇒ 2x² - 2x = 0

⇒ 2x(x - 1) = 0

⇒ x = 0, 1

when x = 0 then y = 0 and when x = 1 then y = 1

∴ Coordinates of end points of diameter AB are (0, 0) and (1, 1)

∴ Required equation of circle with diameter AB

(x - 0)(x - 1) + (y - 0)(y - 1) = 0

⇒ x² - 2 + y² - y = 0

⇒ x² + y² - x - y = 0