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AP EAMCET202119 Aug 2021Morning ShiftMathematicsCircleActual

Find the equations of the tangents drawn to the circle x 2 + y 2 = 50 at the points where the line x + 7 = 0 meets it.

Options

  1. A7 x + y + 50 = 0   &   7 x − y + 50 = 0
  2. Bx + y = 0   &   x − y = 0
  3. Cx + 7 y + 5 = 0   &   y − 7 x + 5 = 0
  4. Dx + 7 y + 50 = 0   &   x − 7 y + 50 = 0

Correct answer

A. 7 x + y + 50 = 0   &   7 x − y + 50 = 0

Step-by-step solution

Given circle x 2 + y 2   =   50 , line x + 7 = 0 ⇒ 49 + y 2 = 50 ⇒ y 2 = 1 So point of intersection is - 7 ,   ± 1 Equation of tangent at x 1 ,   y 1 is x x 1 + y y 1 = r 2 ⇒ - 7 x ± y   =   50 So required equations are 7 x + y + 50 = 0   &   7 x - y + 50 = 0 .

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