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The radius of the circle whose centre is   ( - 4 ,   0 ) and which cuts the parabola y 2 = 8 x at A and B , such that its common chord A B subtends a right angle at the vertex of the parabola is equal to

Options

  1. A4
  2. B3
  3. C18
  4. DNo such circle exist

Correct answer

D. No such circle exist

Step-by-step solution

The centre of the circle is - 4 ,   0 and let r be the radius of the circle. Then, we know that the equation of a circle with centre h ,   k and radius r is x - h 2 + y - k 2 = r 2 Using this the equation of the circle is ( x + 4 ) 2 + y 2 = r 2 . This cuts the parabola at points A x 1 ,   y 1 and B x 2 ,   y 2 Then, we can find the abscissa of A and B by putting the value y 2 = 8 x from the parabola to the circle. Hence, we get an equation ( x + 4 ) 2 + 8 x = r 2 , ⇒ x 2 + 8 x + 16 + 8 x

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