Can someone correct my questions and help me please.

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  • #1
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The line y = x + 2 intersects the curve 4y + 3x^2 = 7 in two places.

a) Find the coordinates of the two points of intersections.

>Sub. y = x + 2 to 4y + 3x^2 = 7
>4(x+2) + 3x^2 = 7
>4x + 8 + 3x^2 -7 = 0
>3x^2 + 4x -1 = 0
>x = -1 and - 1/3
>y = x + 2
>so y = 1 or 5/3

The straight line y = f(x) has gradient 3 and intersects the curve 4y + 3x^2 = 7 at one point only.

b) Find f(x).

>???

c) Hence find the coordinates of the point of intersection between y = f(x) and 4y + 3x^2 =7

>???

:(
 

Answers and Replies

  • #2
10
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to question b)
we know that y = f(x) has gradient 3, so y=3x+m, and 4y+3x^2=7
>4(3x+m)+3x^2=7
>3x^2+12x+4m-7=0
at one point only, so the equation above has only one solution, Δ=0
>m=17/4

q c) is easy ^.^
 
  • #3
13
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Thankyou Very Much!! ^^"
 
  • #4
The line y = x + 2 intersects the curve 4y + 3x^2 = 7 in two places.

a) Find the coordinates of the two points of intersections.

>Sub. y = x + 2 to 4y + 3x^2 = 7
>4(x+2) + 3x^2 = 7
>4x + 8 + 3x^2 -7 = 0
>3x^2 + 4x -1 = 0
>x = -1 and - 1/3
>y = x + 2
>so y = 1 or 5/3

The straight line y = f(x) has gradient 3 and intersects the curve 4y + 3x^2 = 7 at one point only.

b) Find f(x).

>???

c) Hence find the coordinates of the point of intersection between y = f(x) and 4y + 3x^2 =7

>???

:(
i think that alright you aint to old or to young to learn more
 
  • #5
berkeman
Mentor
58,812
8,944
to question b)
we know that y = f(x) has gradient 3, so y=3x+m, and 4y+3x^2=7
>4(3x+m)+3x^2=7
>3x^2+12x+4m-7=0
at one point only, so the equation above has only one solution, Δ=0
>m=17/4

q c) is easy ^.^
Do NOT do the OP's work for them. They are required to do their own homework here at the PF.
 

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