tangent and normals (1 Viewer)

[darshil]

I was doing some excercises from Fitzpatrick relating to tangents and normals of a function. It's really interesting but if possible I need help understanding one question:

9) The straight line y=x+2 cuts parabola y=1/2x6^2-2 at 2 points P and Q. Find the coordinates of P and Q and the coordinates of the point of intersections of these tangents.

It looks like this to me so far:

Thanks for all the help, i really appreciate (truly).

 

[GUSSSSSSSSSSSSS]

yep yep
solve the equation of the line: y = x + 2 (put x + 2 = (1/2)x^2 - 2)
this gives two values for x.
put these 2 values of x back into the original equation (y = x + 2) to find the corresponding y values

differentiate the equation of the parabola: ( dy/dx = x )
then sub in the two values for x, this gives you the respective gradients of the tangents at these points

you can then form the equations of both tangents using the formula: y - y1 = m(x - x1)
and then solve simultaneously


alternatively you can attempt to do the equation parametrically however just stick with the above method, its slightly longer but it is simpler

 

[darshil]

thanks brother ! so the first part gives coordinates of P and Q, then subsequently the derivate gives the two tangents and then you solve them simultaneously to give the intersection !

perfect man !