Question

Find the normal line equations of slope 2 to the ellipse x^2 +2y^2 =3

Answer 1

hint : if the normal at a point has slope of 2, then tangent at that point will have a slope of -1/2

Answer 2

take the derivative, set it equal to -1/2
and u wil get a relation between y and x

Answer 3

aaah! I equated it to 2 instead of -1/2.

Answer 4

why is it equated to -1/2 instead of 2? This is a bit confusing for me

Answer 5

if the question was asking about TANGENT line, then u should be equating it to 2

Answer 6

but the question is asking about NORMAL line equations...

Answer 7

here is the relation :
slope of tangent line = -1/(slope of normal line)

Answer 8

But you said that the slope of the tangent is -1/2 and the slope of the normal line is 2. So if I'm looking for the tangent line equation, shouldn't I be equating it to -1/2? And normal line equation to 2?

Answer 9

good question :)
we already knw the slope of normal = 2

Answer 10

here we're oly trying to find a POINT, at which slope of normal equals 2.

Answer 11

it occurs when the tangent has a slope of -1/2

Answer 12

so take the derivative and set it equal to -1/2

Answer 13

if that makes any sense... :)

Answer 14

On the other hand,
setting the derivative equal to 2, gives u the points at which TANGENT line has slope of 2. NOT THE NORMAL LINE ok ?

Answer 15

GOT IT! THANK YOU SO MUCH!!

Answer 16

np :)