Find equations of common tangents to parabola y^2=15x, circle x^2+y^2=16

phil89

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Oct 16, 2016
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Hi everyone!

I'm having some troubles resolving one last point of my weekly sheet.The text says:
"Find the equations of the common tangents to the parabola y^2=15*x and the circle x^2+y^2=16."

I tried the approach of the discriminant and also one using the distance from a line but both didn't work for me. A previous exercise asked me to demonstrate that the line y=mx+(15/4m) is a tangent to the parabola for every value of m. A suggestion in the text says I can use this result also to find the common tangent.
 
"Find the equations of the common tangents to the parabola y^2=15*x and the circle x^2+y^2=16."

I tried the approach of the discriminant and also one using the distance from a line but both didn't work for me. A previous exercise asked me to demonstrate that the line y=mx+(15/4m) is a tangent to the parabola for every value of m. A suggestion in the text says I can use this result also to find the common tangent.
Please reply showing what you've tried, so we can see what's going on and check for any errors. Thank you! ;)
 
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