Question

The line 3 x + 5 y is equal to k touches the ellipse 16 x square + 25 y square is equal to 400 if k is

Answer 1

Answer:

Step-by-step explanation:

Dude go as follow :-

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

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