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# Engineering

If the line y=mx+c is a common tangent to the hyperbola \frac{x^2}{100}-\frac{y^2}{64}=1 and the circle x^2+y^2=36 then which of the following is true?
Option: 1 4c^2=369
Option: 2 5m=4
Option: 3 8m+5=0
Option: 4 c^2=369

Answers (1)
H Himanshu Meshram

Equation of the circle x^2+y^2=36

Equation of a tangent to the circle y=mx\pm6\sqrt{1+m^2}

Equation of Hyperbola y=mx\pm\sqrt{100m^2-64}

For the common tangent

\\36(1+m^2)=(100m^2-64)\\64m^2=100\\m^2=\frac{100}{64}\\Now, c=6\sqrt{1+m^2}=\\c^2=36(1+m^2)=\frac{369}{4}\\4c^2=369

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