The question is: Find the equations of the tangent lines to the curve y = 2x^2 + 3 That pass through the point (2, -7)
The last time I did this sort of questions was over a year ago and I think I remember that you're supposed to pick a point (a, f(a) ) on the parabola first, and go from there. But what then? How would you find the slope from (2, -7) to a point you don't know?
Ok, you have picked point (a, f(a) ) on the parabola. So, of course you can find the slope in term of a. You also can find the coordinate where the parabola and tangent meet, in term of a.
Find the tangent (still consists of a), then do something with the tangent and (2, -7) ^^
Hmm I gave it a go but I think I'm doing it wrong.
So the slope of the tangent is 4a
and the x co-ord of the tangent on the line is a, and the y co-ord is 2a^2+3.
So I made the tangent y+7=4a(x-2) --> 2a^2+3+7=4a(a-2)
and I solved that and I got 2 a values: (-4+sqrt(8))/2 and (-4-sqrt(8))/2
So then I took the first a value and calculated f(a) = 3.68
So now I did f(a)-y/a-x ---> 3.68+7/-0.585-2 = -4.13 (slope)
Tangent is y+7 = -4.13(x-2) ?
When I put this tangent into the graphing program I have it cuts the curve at 2 points (close together though) so is this not the tangent? Can someone tell me how to do it lol.