Question

-300x(-12)+(-300)x(2) give full expiation full​

Answer 1

Step-by-step explanation:

-300x(-12)+(-300)x(2)

= 3600 - 600

= 3000

Answer 2

From the given equation of the curve 300x

2

+320xy+144y

2

−1220x−768y+199=0, we have

A=300,H=160,B=144

Here, AB−H

2

>0

Thus, the given curve is of ellipse

To find center of the curve, partially differentiate it w.r.t x and w.r.t y

30x+16y=61

10x+9y=24

Solving for x and y, we get

Center of the ellipse as (1.5,1)

Take x=X+1.5

and y=Y

300X

2

+320XY+144Y

2

=1100

We need to eliminate the term XY

For eliminating the term XY, we need to find the degree of rotation of the axis

i.e. tan2θ=

A−B

H

i.e. tan2θ=

300−144

320

⇒θ=32

o

X=ucosθ−vsinθ

Y=usinθ+vcosθ

Substituting the value of θ and expressing the equation in the form of u and v.

The equation will be:

2.76

u

2

+

25

v

2

=1

Now the foci can be easily find as (−1,5) and(4,−3).