maths c2 edexcel

[astarmathsandphysics]

1 hour

[astarmathsandphysics]

find the coordinates of the point where the tangent to the curve y=x^2 + 1  at the point (2,5)
meets the normal to the same curve at the point (1,2)
tangent to curve y=x^2 + 1  dy/dx=2x=2*2=4
y-5=4(x-2) so y=4x-3 (1)
normal at (1,2) has gradient -1/2*1=-1/2
y-2=(-1/2)(x-1) so y=-0.5x+2.5 (2)
(1) -(2) gives 0=4.5x-5.5 so x=9/11 and from (1) y=4*9/11 -3=3/11
(9/11,3/11)

[halosh92]

find the coordinates of the point where the tangent to the curve y=x^2 + 1  at the point (2,5)
meets the normal to the same curve at the point (1,2)
tangent to curve y=x^2 + 1  dy/dx=2x=2*2=4
y-5=4(x-2) so y=4x-3 (1)
normal at (1,2) has gradient -1/2*1=-1/2
y-2=(-1/2)(x-1) so y=-0.5x+2.5 (2)
(1) -(2) gives 0=4.5x-5.5 so x=9/11 and from (1) y=4*9/11 -3=3/11
(9/11,3/11)

how did you find the gradient of the normal..on wat basis did u come up with these equation? (normal at (1,2) has gradient -1/2*1=-1/2
y-2=(-1/2)(x-1) so y=-0.5x+2.5 )

[astarmathsandphysics]

Dy/dx=2x and x=1 so dy/dx=2 and gradient of normal=-1/2