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Parametrics (1 Viewer)

phoenix159

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The normals to the parabola x2 = 4Ay at the points P1 and P2 intersect at Q. If the chord P1P2 varies in such a way that it always passes through the point (0, –2A), show that Q lies on the parabola.
 

HeroicPandas

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Step 1: Read question
Step 2: Draw diagram
Step 3: Read question again
Step 4: Identify an aim
Step 5: Work towards your aim by using information given
 

HeroicPandas

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What is your aim Mr Pheonix?! Show that Q lies on the parabola right? That means Q must satisfy the parabola right?(keep this in your mind)

What is Q? It is the intersection between the normals at P1 and P2. Find the point of intersection of these normals to find Q

If we sub in Q into the parabola, we'll need to show that LHS = RHS to show that it satisfies it --> We are not going to sub in Q yet as it looks very BAD --> Q( -ap1p2(p1 + p2), 2a + a(p12 + p1q2 + p22)

Read the question again, notice that it says the line P1P2 must intersect (0,-2a) --> This means (0,-2a) satisfies the EQUATION P1P2

Workout equation P1P2, sub in (0,-2a) to get a relationship between p1, p1, p2 , q1 and q2 --> Use this to manipulate the point Q and then we can proceed to subbing it into the parabola to show it satisfies
 

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