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Bài tập CALCULUS 47
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Created by T. Madas
Question 170
(****)
The curve C and the straight line L have respective equations
y = 2 x2 − 6 x + 5
and
2y + x = 4 .
a) Find the coordinates of the points of intersection between C and L .
b) Show that L is a normal to C .
The tangent to C at the point P is parallel to L .
c) Determine the x coordinate of P .
C1L ,
Created by T. Madas
,
( 2,1) , ( 34 , 13
8)
xP = 11
8
Created by T. Madas
Question 171
(****)
y
y=
16
x2
R
O
x
y = 17 − x 2
The figure above shows the graphs of the curves with equations
y=
16
x
2
and
y = 17 − x 2 .
The finite region R , shown shaded in the figure above, is bounded by the two curves
in the first quadrant.
Find the area of R .
SYN-E , 18
Created by T. Madas
Created by T. Madas
Question 172
(****)
The curve C and the straight line L have equations
C : y = x 2 − 10 x + 23 and L : y = 1 x − 3 .
2
a) Find an equation of the tangent to C at the point P , where x = 4 .
b) Determine the coordinates of the points of intersection between L and C .
c) Show that L is a normal to C .
(
C1H , y = −2 x + 7 , P ( 4, −1) , Q 13 , 1
2 4
Created by T. Madas
)
