Question

Question 4 g A-2 B 6 0 The sketch shows a circle, a parabola, which is the graph of f, and a straight line, which is the graph of g. The parabola has x-intercepts –2 and 6, and y-intercept 6. Its turning point is C. The circle has its centre at the origin and it passes through the point A, which has coordinates (-2,0). At point B both the circle and the straight line cut the x-axis. The straight line has y-intercept 1.

Answer 1

с 10,6) А 8(2,0) →x 116,0) .. 2 Stepl: calculate the equation of parabola : Assume that the equation of parabola is y= an + bate since, parabola passes through the 0 = 4a-2b + c the then point (-2,0) (6,0), :: parabola passes through point o = 36 a to btc then parabola passes through point 10,6) then 6=0

Thus, have we obtained the following system: 4a 2 b +c=0 3a + obtc=0 c=6 ON we get solving b=é, c=6 a=-1 2 Thus, the equation of parabola is 19 • -+ 2x+5 (y-8)= - + (x-2) 07 2 line or Curve 8: line be: let the of Equation of straigh equation y passes through 11 = 0 matc (0,0) .. line point copy & (2,0) then & 0= 2mtc m = -ld Thus, equation of line : 1 Tout I Ź y

Step 2 Calculate the coordinate C 2 y -ntzut 6 2 dy an +2 da 2 → -ut 2–0 10=2 dy dn =0 → At 2=2 (203 y = + 2(2) + 6 = 4 + 4 +6 = -24476 2 2 8 Thus, coordinate c (2,8) can A(-2,0) c(2,8) (X,Y,) (x2,42) two points between • Distance be expressed as: d = [ (x2-x)² + (ya-y,j? [ (2+2)² + (8-03² » Distance b/w Ac= 16 +64 Гео son Distance b/w Ac = 8.944 Answer (a)

(6) Midpoint of AC 0+8 01-242, 0 2 D(0,4) so - (C) diameter of circle 28= √ 80 -> 180 2 is the centre of circle. & Midpoint (D) circle Then , is given by: of Equation 2 + (2-052 (4-4)² sou 2 2 こ 20 > u + (9-4) 4.7 graph f: ya + 2x+6 : y = - + 1 graph vertical distance b/w f & g graph hem + 247 5)-(4+1)

+20+6+44-1 +5 Vertical distance = ***+51 - 9+ Calculation 0F distance . Max. vertical vertical distance Find the derivative of to zero. set equal it equation & - 2n 쯤 들 tono 2 u=2-5 (ii) the value of u=2.5 in in original Plug Equation 2 so, Maximum vertical distance = -(2-5) 5 (2.5) 75 2 2 8:125 (4-8) ut [-2,2 [6,00)