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NTA Abhyas JEE Main2020MathematicsCirclePractice

The extremities of a diagonal of a rectangle are 0,0 and 4,3 . The equations of the tangents to the circumcircle of the rectangle which are parallel to the diagonal are

Options

  1. A3 x - 4 y = ± 5
  2. B3 x + 4 y = ± 10
  3. C3 x + 4 y = ± 25
  4. D6 x - 8 y = ± 25

Correct answer

D. 6 x - 8 y = ± 25

Step-by-step solution

Let, A B C D be the rectangle such that the coordinates of the vertices A and C of diagonal A C are A 0,0 and C 4,3 . The equation of the circumcircle of rectangle A B C D is x - 0 x - 4 + y - 0 y - 3 = 0 ⇒ x 2 + y 2 - 4 x - 3 y = 0 … 1 The equation of a line parallel to A C is 3 x - 4 y + λ = 0 … 2 If it touches the circle 1 , then λ 9 + 16 = 4 + 9 4 ⇒ λ 5 = 5 2 ⇒ λ = ± 25 2 Substituting the value of λ in 2 , we obtain that the equations of the required

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