Question

In the equation x^2+y^2-9x+8y=5, at what points is the the tangent line horizontal? vertical?

The curve has a ___horizontal or vertical____ tangent line when x=_____.

The curve has a __horizontal or vertical____ tangent line when y=______.

Please explain:) thank you!!

and also, dy/dx of the equation is (9-2x)/(2y+8)

:)

Answer 1

It all boils down to what you know about the derivative dy/dx and how it relates to the tangent line.

dy/dx is the *slope* of the tangent line, yes?

Answer 2

yes:)

Answer 3

Simple. A horizontal line has a zero-slope.
A vertical line has an undefined slope.
So... for what values of x and y would the slope dy/dx be zero?

Answer 4

how would i find that?

9-2x=0 solve for x?

and 2y+8=0 solve for y?

Answer 5

Don't touch the denominator yet, we're still on the horizontal tangent line.
To make a fraction zero, it suffices to make the numerator equal to zero.

So yes, 9 - 2x = 0 and solve for x will give you the x-values that give a horizontal tangent line.


On the flipside, an undefined tangent line occurs when the denominator is zero, so to get the values that give a vertical tangent line, solve
2y + 8 = 0 and solve.

^_^

Answer 6

ohh okay...

so right now, just solving for x?

so -2x=9 so x = -2/9?

Answer 7

oops... try again

Answer 8

oh oops haha x= -9/2 ?

Answer 9

no.
Take a deep breath and solve
9 - 2x = 0
again...

Answer 10

ohh okay... umm lol oops... my bad :P