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

Find the equations of the tangents drawn to the circle x2+y2=50 at the points where the line x+7=0 meets it.
  1. 7x+y+50=0 & 7x−y+50=0
  2. x+y=0 & x−y=0
  3. x+7y+5=0 & y−7x+5=0
  4. x+7y+50=0 & x−7y+50=0

Solution

Given circle x2+y2 = 50, line x+7=0

⇒49+y2=50

⇒y2=1

So point of intersection is -7, ±1

Equation of tangent at x1, y1 is xx1+yy1=r2

⇒-7x±y = 50

So required equations are 7x+y+50=0 & 7x-y+50=0.

Asked in: AP EAMCET 2021 (19 Aug Shift 1)

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