Question

Show that the line x - y+4=0 is a tangent to the ellipse x^2 + 3y^2 = 12. Also find the coordinates
of the point of contact.​

Answer 1

Answer:

he given ellipse is x2 + 3y2 = 12  (÷ by 12) ⇒ (x2/12) + (y2/4) = 1 (ie.,) Here a2 = 12 and b2 = 4  The given line is x – y + 4 = 0  (ie.,) y = x + 4  Comparing this line with y = mx + c We get m = 1 and c = 4  The condition for the line y = mx + c  To be a tangent to the ellipse (x2/a2) + (y2/b2) = 1 is  c2 = a2 m2 + b2  LHS = c2 = 42 = 16  RHS: a2 m2 + b2 = 12(1)2 + 4 = 16  LHS = RHS  The given line is a tangent to the ellipse. Also the point of contact is (i.e.,) (-3, 1)Read more on Sarthaks.com - https://www.sarthaks.com/872975/show-that-the-line-tangent-to-the-ellipse-12-also-find-the-coordinates-the-point-of-contact

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