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# If the line $y=mx+c$ touches the hyperbola $\large\frac{x^2}{a^2}+\frac{y^2}{b^2}$$=1 then find the value of c . \begin{array}{1 1}(a)\;\pm \sqrt{a^2m^2-b^2}\\(b)\;\pm \sqrt{a^2m^2+b^2}\\(c)\;\pm \sqrt{b^2m^2-a^2}\\(d)\;\text{None of these}\end{array} Can you answer this question? ## 1 Answer 0 votes Toolbox: • For equal roots of the quadratic equation Ax^2+Bx+c=0, Discriminant B^2-AC=0 Given Equation of the hyperbola is \large\frac{x^2}{a^2}-\large\frac{y^2}{b^2}$$=1$...(i)
Also given that $y=mx+c$......(ii) is tangent to the hyperbola
Solving (i) and (ii) we get