Maths second part of conic sections Q

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Ogaar
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I’ve done part i) but can’t figure out how to do part ii)
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RDKGames
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(Original post by Ogaar)
I’ve done part i) but can’t figure out how to do part ii)
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You know that for all m\neq 0 your line is tangent to the parabola.

Now go ahead and find all the m values for which the line is tangent to the circle.
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Ogaar
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(Original post by RDKGames)
You know that for all m\neq 0 your line is tangent to the parabola.

Now go ahead and find all the m values for which the line is tangent to the circle.
I subbed y^2 into x^2 + y^2 = 16 and ended up solving for x and got x = 1 and x= -16 but how does this get the answer?
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RDKGames
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(Original post by Ogaar)
I subbed y^2 into x^2 + y^2 = 16 and ended up solving for x and got x = 1 and x= -16 but how does this get the answer?
Think about what you just calculated ... was this the right thing to do?
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Ogaar
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(Original post by RDKGames)
Think about what you just calculated ... was this the right thing to do?
What else can you really do with what you’re given? Maybe differentiate?
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DFranklin
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(Original post by Ogaar)
What else can you really do with what you’re given? Maybe differentiate?
So, let's be clear: you took the y^2 = 15x equation and substituted into x^2+y^2 = 16 and solved.
What does this give you?
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The points where the two curves intersect.

And is this what the question is asking for? [Spoiler: No].

Instead, you should basically be doing something similar to (i) again, but for the circle. This time you won't find the discriminant = 0 for all values of m, but the values of m where it does equal 0 for will define lines tangent to both shapes simultaneously.
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Ogaar
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(Original post by DFranklin)
So, let's be clear: you took the y^2 = 15x equation and substituted into x^2+y^2 = 16 and solved.
What does this give you?
Spoiler:
Show
The points where the two curves intersect.

And is this what the question is asking for? [Spoiler: No].

Instead, you should basically be doing something similar to (i) again, but for the circle. This time you won't find the discriminant = 0 for all values of m, but the values of m where it does equal 0 for will define lines tangent to both shapes simultaneously.
Thank you, got it
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Ogaar
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(Original post by DFranklin)
So, let's be clear: you took the y^2 = 15x equation and substituted into x^2+y^2 = 16 and solved.
What does this give you?
Spoiler:
Show
The points where the two curves intersect.

And is this what the question is asking for? [Spoiler: No].

Instead, you should basically be doing something similar to (i) again, but for the circle. This time you won't find the discriminant = 0 for all values of m, but the values of m where it does equal 0 for will define lines tangent to both shapes simultaneously.
Thank you, got it
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