|
Question 1028387: if the line 3x+5y=k touches ellipse 16x^2+25y^2=400, then what is value of k
Answer by Alan3354(69443)   (Show Source):
You can put this solution on YOUR website! if the line 3x+5y=k touches ellipse 16x^2+25y^2=400, then what is value of k
----------
The slope of the line, m = -3/5
----
Find the slope of the ellipse 16x^2+25y^2=400
--
16x^2+25y^2=400
differentiate implicitly
32x*dx + 50y*dy = 0
dy/dx = -32x/50y
---
-16x/25y = -3/5
80x = 75y
y = 16x/15
-----------
16x^2+25y^2=400
Sub for y
16x^2+25(16x/15)^2=400
16x^2+25(256x^2/225)=400
16x^2+ 256x^2/9 = 400
400x^2 = 3600
x = ±3
------------
--> (3,3.2)
3x+5y=k
9 + 16 = k
k = 25
-------------
and (-3,-3.2)
-9 - 16 = k
k = -25
--------
|
|
|
| |
