Question

Can someone help to walk me through the steps for this!
Find an equation of the tangent line to the parabola at the given point.
x2 = 9y, (–7, 49/9)
______________
Find the x-intercept of the line.
(x,y)=(_________)

Thanks!

Answer 1

the equation of the parabola is \[x ^{2}=9y\] ??

Answer 2

yes

Answer 3

Do you know the equation of the tangent lines of the parabola?
If you have this equation \[(x-h)^2=4p(y-k)\] the equation is:
\[(x _{0}-h)(x-h)=4p \left[ \left( \frac{ y+y _{0} }{ 2 } -k \right) \right]\]
you have one point , so replace in xº and yº
(x)(-7) = 9[(y+49/9)]/2
operating..
-14x=9y+49
(-49-14x)/9=y
So the slove is -14/9 and the intercept -49/9

Answer 4

Ok! I kind of get how you solved the equation, but how did you find the x-intercept?

Answer 5

iam sorry

Answer 6

i give you the intercept with y

Answer 7

x^2 = 9y
y = 1/9 * x^2
Slope = dy/dx = 2/9 * x
slope at (–7, 49/9) put x = -7 above
slope - 2/9 * (-7) = -14/9

You know the alope of the tangent line and you know one point (–7, 49/9)

Find the equation of the line: y = mx + b
y = -14/9x + b
x = -7, y = 49/9
49/9 = -14/9 * (-7) + b
49/9 = 98/9 + b
b = 49/9 - 98/9 = (49-98)/9 = -49/9

y = -14/9x - 49/9

They are asking for the x-intercept (NOT the y-intercept).
To find the x-intercept set y = 0 and solve for x
0 = -14/9x - 49/9
14/9x = 49/9
x = 49/9 * 9/14 = 49/14
x intercept = 49/14

Answer 8

if you want the intercept of x , put 0 in y

Answer 9

For some reason, it keeps getting marked wrong! But the equation is right and I'm starting to understand the concept a little bit better. Thank you so much you two!

Answer 10

oops. sign mistake. x-intercept = -49/14

Answer 11

That worked :) Thank you!

Answer 12

you are welcome.