If the line y = m x + 1 is a tangent to the ellipse x2 + 4 y2 =1 then find the value of m 2

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Please find below the solution to the asked query:

We have y=mx+1x2+4y2=1x21+y214=1We know that y=mx+c is tangent to ellipse x2a2+y2b2=1 a>b if c2=a2m2+b2Here c=1, a2=1 and b2=141=m2+14m2=1-14m2=34m=±32

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