The homogeneous function of the second degree in x and y having $2 x - y$ as a factor, taking the value 2 when $x = y = 1$ and vanishing $x = - 1, y = 1$ is:

2 x^{2} - x y - y^{2}

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

3 x^{2} - 2 x y + y^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

x^{2} + x y - 2 y^{2}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

none of these

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is A $2 x^{2} - x y - y^{2}$
The homogeneous function of second degree is $f (x, y) = a x^{2} + b y^{2} + 2 h x y$

Using the given conditions, we get
$a = 2, b = - 1 a n d 2 h = - 1$

Satisfies for $\Rightarrow 2 x^{2} + x y - y^{2}$

Suggest Corrections

Similar questions

t a n \frac{1}{2} [s i n^{- 1} \frac{2 x}{1 + x^{2}} + c o s^{- 1} \frac{1 - y^{2}}{1 + y^{2}}]

| x | < 1, y > 0 a n d x y < 1

x^{2} y^{2} + x y + 1

x = 3

y = 2

x^{2} - x y + y^{2}

P_{1}, P_{2}, P_{3}

(0, 0)

x y + x + y + 1 = 0

x^{2} - y^{2} + 2 x + 1 = 0

2 x^{2} + 3 x y - 2 y^{2} + 3 x + y + 1 = 0

Join BYJU'S Learning Program