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MHT CET2018MathematicsCircle

The sides of a rectangle are given by x = ± a and y = ± b . Then equation of the circle passing through the vertices of the rectangle is

Options

  1. Ax 2 + y 2 = a 2
  2. Bx 2 + y 2 = a 2 + b 2
  3. Cx 2 - y 2 = a 2 - b 2
  4. Dx - a 2 + y - b 2 = a 2 + b 2

Correct answer

B. x 2 + y 2 = a 2 + b 2

Step-by-step solution

Now Equation of circle (a, b) and (-a, -b) as extremities of its diameter is ( x − a ) ( x + a ) + ( y − b ) ( y + b ) = 0 ⇒ x 2 − a 2 + y 2 − b 2 = 0 ⇒ x 2 + y 2 = a 2 + b 2

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