C2 Maths Exam Question Help Exam Tommorow

vv2006

Hey really stuck on this

Its number 8 of AQA AS Maths Core 2 January 2006.

A curve, drawn from the origin O, crosses the x axis at the point A(9,0). Tangents to the curve at O and A meet at the point P, as shown in the diagram.

diagram O p a(9,0)

a. Find dy/dx done

b. Find the value of dy/dx at the point O and hence write down an equation of the tangent at 0.

bii. Show that the equation of the tangent at A(9,0) is 2y= 3x - 27 (i;m stuck!)

iii. Hence find the co ordinates of the point P where the two tangents meet.

(and no i dont have a scanner, sorry)

Reply 1

zrancis

bii) Use

y-0=\frac{dy}{dx}(x-9)

Reply 2

vv2006

Could you explain how you get that please

Reply 3

chidona

Use the General rule:

(y - y_1 ) = \frac{dy}{dx} (x - x_1 )

Find the value of the gradient when x = 9, plug it in, and off you go.

Reply 4

barry_4_england

It's just a standard equation. dy/dx= (y-y1)/(x-x1), using x=9 and y=0.

Reply 5

vv2006

I am stuck on part iii

please help

Reply 6

Mah

Use the two equations you have as simultaneous equations.

2y= 3x-27
y= -3x +

Gives you 3y= -27

So y is -9, put that back into one of the equations to get x which is 3 :cool:

Reply 7

vv2006

So stuck on this.

Calculate the area of the shaded region bounded by the curve and the tangents OP and AP.

PART OF THE SAME QUESTION.

Reply 8

Mah

To find area under the curve you've got to integrate between 9 and 0 the equation given in the integration question. This gives you -24.3 . Then find the area of the triangle which is 0.5x9x9 giving you 40.5. 40.5 - 24.3 is 16.2 which is the answer.