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Show that the line y=mx+c touches the cu...

Show that the line y=mx+c touches the curve `x^2/a^2-y^2/b^2 = 1` if `c^2=a^2m^2-b^2`

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Show that the line y = mx + c touches the ellips x^2/a^2 + y^2/b^2 = 1 if c^2 = a^2m^2 + b^2 .

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Show that the line y = mx + c touches the parabola y^(2) = 4ax if c = (a)/(m) .

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If the straight line x cos alpha + y sin alpha = p touches the curve (x^(2))/(a^(2)) + (y^(2))/(b^(2)) = 1 , then prove that a^(2) cos^(2) alpha + b^(2) sin^(2) alpha = p^(2) .

Prove that y=mx+c touches the parabola y^2 = 4ax if a=mc .

Show that the condition that the curves ax^(2) + by^(2) = 1 and a_(1)x^(2) + b_(1)y^(2) = 1 should intersect orthogonally such that (1)/(a) - (1)/(b) = (1)/(a_(1)) - (1)/(b_(1)) .

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