Question

Bo Find equations of the vertical lines that meet the curves (a) y = x + 2x - 4x+5 and (b) 34= 2 x + 9x -3x-3 in points at which the tangent lines to the two curves are parallel. tion: @ y = x + 27 - 4x + 5

Mathematic please i need a help

Answer 1

Solution: Page 1 Curve the curves f(n) - Y = x² + zn²-40+5 g (1) >34 = 2x² + 9m²-32-3 We need equation of verfical lines that meet fln) of g(n) at points at which tangents to the corres are parallel slope of fangent of y = f(2) = slope of fangent of y= g(x) >> y = $(x) = }+2*-44+5 f'(x) = 3% +40-4 Hence, g (n) = $ ( 23'+ 2ri'+901-34-3 - 2x + 6H-1 g'(x) 3) t'(1) = (n) => 34+48-4-20?+67-1 212-274-3 = 0 =) (0-3)(x+1) =0 -) NE-1 & x=3

So, At 21 - parallel -1+2+4+5 =10 27+ 18-12+5=38 o'. on Page 2 & [2=3 tangents to the both curves are So, finding the co-ordinates of point of tangent y = f(n) = + 2n? -44+5 $(-1) 6 (3) p(-1,60) $ Q (3,38) f(n) y = g(n) = { (23*+ 9x?-34-3) g (-1) = ķ (-2+9+3-3) = 773 9(3) = {( 54+81-9-3) - ” : *(-1,%) +5(3,9 Now, the equation of vertical line passes through P&R =122-11 Also, equation of vertical line passing through 123 xtl=0 Q & s 1-3 20 Y-3 Auswer

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