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Maths second part of conic sections Q

I’ve done part i) but can’t figure out how to do part ii)
7926DC89-3245-4980-BBA8-E7C839ADD052.jpeg
Original post by Ogaar
I’ve done part i) but can’t figure out how to do part ii)
7926DC89-3245-4980-BBA8-E7C839ADD052.jpeg

You know that for all m≠0m\neq 0 your line is tangent to the parabola.

Now go ahead and find all the mm values for which the line is tangent to the circle.
Reply 2
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Ogaar
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Original post by RDKGames
You know that for all m≠0m\neq 0 your line is tangent to the parabola.

Now go ahead and find all the mm 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?
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?
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?

Spoiler


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


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
Reply 7
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Ogaar
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9
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


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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