parametrics qn (1 Viewer)

[blakwidow]

Tangents are drawn from the point

to the parabola

. P and Q are the points of contact of the tangents.

a) Find the equation of the chord PQ

b) Show that the x-coordinate of P and Q are the roots of the quadratic

From part a) x = -1

subbing into quad. = 0 (approx.)

c)Find the sum of the roots of the equation in part b)

Using quad. formula roots are -1 and 5
therefore sum = 4

d) Hence, find the midpoint M of the chord PQ, and show that TM is // to the axis of the parabola

How is part (d) related to part (c)

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(i) Write down the equation of the chord of contact of the parabola from the point



(ii) Suppose that the points of contact of the tangents are A and B. Find a quadratic equation whose roots are on the x-coordinates of A and B

 

[Bank$]

just by skimming through i suspect that that the end points of the chords are irational numbers and so when u use the midpoint formula and have to add them it will be hard. So by using the sum of the roots it is easy as it will give u a simple value of 4.

 

[blakwidow]

but what does the roots in the quadratic have to do anything with the chord??

 

[Bank$]

because:
when u equate the equation of the chord and parabola u will get a quadratic equation where the points of intersection or in this case the end points are the roots of that eqaution and when finding the x ordinate for the midpoint u must divide THE SUM of the x ordinates (i.e roots of that quadratic) and divide by 2.