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MHT CET2019Evening ShiftMathematicsCircleActual

The intercept on the line y = x by the circle x 2 + y 2 - 2 x = 0 is A B . The equation of the circle with A B as a diameter is ……

Options

  1. Ax 2 + y 2 + x + y = 0
  2. Bx 2 + y 2 - x - y = 0
  3. Cx 2 + y 2 - 3 x + y = 0
  4. Dx 2 + y 2 + 3 x - y = 0

Correct answer

B. x 2 + y 2 - x - y = 0

Step-by-step solution

We have equation of line y = x and equation of circle x 2 + y 2 - 2 x = 0 Now, intersecting points of given line and circle x 2 + x 2 - 2 x = 0 ⇒ 2 x 2 - 2 x = 0 ⇒ 2 x x - 1 = 0 ⇒ x = 0,1 When x = 0 then y =0 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 ⇒ x 2 - 2 + y 2 - y = 0 ⇒ x 2 + y 2 - x - y = 0

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