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The parabola \(y = x^2+2\) and the hyperbola \(y^2 - mx^2 = 1\) are tangent. Find \(m.\) 

 Mar 9, 2019
 #1
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Hyperbolas and parabolas are not tangents. That makes no sense.

I assume you mean that they only touch each other in one place. Which means they have only one simultaneous solution.

 

I would try making x^2 the subject of the formula for the first equation.

then

substitute this value of x^2 inot the second equation.

then

solve the new equation as an quadratic.  You may then have 2 values for y  (in terms of m)

and

etc

 

Try that and get back with what you have done.

 

 

 No one answer over me. Thanks 

 Mar 9, 2019

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