Bài tập CALCULUS 47

Created by T Madas Question 170 (****) The curve C and the straight line L have respective equations y = x2 − x + and 2y + x = 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 Created by T Madas Question 171 (****) y y= 16 x2 R O x y = 17 − x The figure above shows the graphs of the curves with equations y= 16 x and y = 17 − x 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 − 10 x + 23 and L : y = x − a) Find an equation of the tangent to C at the point P , where x = 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 + , P ( 4, −1) , Q 13 , Created by T Madas )