Question

8.

The transformed equation of 4xy - 3x2 =10

when the axes are rotated through an angle

whose tangent is '2' is








Can someone please help me with this question

I will mark you as the brainliest

Answer 1

Answer:

4xy-3×2=10

4xy-6=10

4xy=10+6

4xy=16

xy=16÷4

xy=4

Explanation:

CHECKING:

Only you have to insert the answer that just we got i.e : 4 In the question like :

we got xy: 4

4×4-3×2=10

16-6=10

Now,solve 16-6

10=10

Therefore, we got the right answer.

Now,please mark me as Blainliest

Answer 2

Answer:

The transformed equation is $X^{2} -4Y^{2} =10$.

Explanation:

Given equation is $4 x y-3 x^{2}=10$

We know that,

$x=X \cos \theta-Y \sin \theta$

$y=X\sin \theta+Y\cos \theta$

Given $\tan \theta=2$

$\sin \theta=\frac{2}{\sqrt{5}}, \cos \theta=\frac{1}{\sqrt{5}}$

$\Rightarrow \mathrm{x}=\frac{1}{\sqrt{5}}(\mathrm{X}-2 \mathrm{Y}) \text { and } \mathrm{y}=\frac{1}{\sqrt{5}}(2 \mathrm{X}+\mathrm{Y})$${x}=\frac{1}{\sqrt{5}}({X}-2 {Y}) \text { and } {y}=\frac{1}{\sqrt{5}}(2 {X}+{Y})$

So, the transformed equation is

$\frac{4}{5}(X-2 Y)(2 X+Y)-\frac{3}{5}(X-2 Y)^{2}=10$

$X^{2}-4 Y^{2}=10$

Hence, the transformed equation is $X^{2}-4 Y^{2}=10.$