[bigbadb1319]

Hi, does n-e-1 know how to do this:

Q10) ex. 2b C4 edexcel:

Find the points of intersection of the parabola x=t², y=2t, with the circle
x² + y² - 9x + 4 = 0

i know that you gotta change this bit x² + y² - 9x + 4 = 0 into da eq. of a circle but dats where i'm stuck!
thanx...
-u.b

[Christophicus]

Originally Posted by bigbadb1319

Hi, does n-e-1 know how to do this:

Q10) ex. 2b C4 edexcel:

Find the points of intersection of the parabola x=t², y=2t, with the circle
x² + y² - 9x + 4 = 0

i know that you gotta change this bit x² + y² - 9x + 4 = 0 into da eq. of a circle but dats where i'm stuck!
thanx...
-u.b

it's easier than that.
sub x = t², y = 2t into x² + y² - 9x + 4 = 0 and solve the quadratic equation to find values of t. Then sub these values back into equations for x and y in terms of the parameter t.

[samd]

x² + y² - 9x + 4 = 0
=> (x - 4.5)² + y² = 16.25

That I think is "da equation of a circle" you're after.

[bigbadb1319]

hey thanx....i get the x - 4.5 bit, but how did u manage to get y + 2?

[Malik]

Originally Posted by Widowmaker

it's easier than that.
sub x = t², y = 2t into x² + y² - 9x + 4 = 0 and solve the quadratic equation to find values of t. Then sub these values back into equations for x and y in terms of the parameter t.

t⁴+4t²-9t²+4=0
t⁴-5t²+4=0
(t²-1)(t²-4)
t=±1 t=±2

x=t²
x=1 and x=4

y=2t
y=±2 and y=±4

.:. intersect at (1,2) (1,-2) (4,4) (4,-4)

[bigbadb1319]

Originally Posted by Malik

t⁴+4t²-9t²+4=0
t⁴-5t²+4=0
(t²-1)(t²-4)
t=±1 t=±2

Thanx....
-u.b