If the line y = 2 x + c touches the curve x 2 + 4 y 2 = 4 , then c 2 =

If the line y=2x+c touches the curve x2+4y2=4, then c2=
  1. 65
  2. 17
  3. 63
  4. 8

Solution

y=2x+c is tangent to ellipse x24+y21=1

Tangent : y=mx±4m2+1

On comparing

m=2, c2=4m2+1

⇒c2=17

Asked in: AP EAMCET 2020 (23 Sep Shift 1)

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