$2 x^{2} + 3 y^{2} - 5 x y + 5 x - 5 y = 0$
This is the equation of a

parabola

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

pair of straight line

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

ellipse

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

hyperbola

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

Open in App

Solution

The correct option is B pair of straight line
General equation of a conic is $a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0$
$\Rightarrow$ It will represent $a$ pair of straight line if
$∣ ∣ ∣ ∣ \begin{matrix} a & h & g h & b & f g & f & c \end{matrix} ∣ ∣ ∣ ∣ = 0$

Equation: $2 x^{2} + 3 y^{2} + 5 x y + 5 x - 5 y = 0$

$∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} 2 & - \frac{5}{2} & \frac{5}{2} - \frac{5}{2} & 3 & - \frac{5}{2} \frac{5}{2} & \frac{- 5}{2} & 0 \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣ ∣ ∣ = 2 (0 - \frac{25}{4}) + \frac{5}{2} (0 + \frac{25}{4}) + \frac{5}{2} (\frac{25}{4} - \frac{15}{2})$ [expanding along first row]

$= - \frac{25}{2} + \frac{125}{8} + (- \frac{25}{8}) = \frac{100}{8} - \frac{25}{2}$ .

$= 0$

$∴$ It represents a pair of straight lines
Hence, option (B) is correct.

Suggest Corrections

Similar questions

Q. The equation of the asymptotes of the hyperbola

2 x^{2} - 5 x y - 3 y^{2} - 5 x - 3 y - 21 = 0

differ by

λ

then

λ = ?

Equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of straight lines. If their point of intersection is (h,k) find the value of h-k.

Q. Assertion :The equation of the pair of straight lines passing through the origin and perpendicular to the straight lines

2 x^{2} + 5 x y + 2 y^{2} + 10 x + 5 y = 0

2 x^{2} - 5 x y + 2 y^{2} = 0

Reason: If

m

be the slope of a given line, then the slope of a line

⊥^{e r}

to it is

- \frac{1}{m}

Equation $2 x^{2} + 5 x y + 3 y^{2} + 6 x + 7 y + 4 = 0$ represents a pair of straight lines. Find the separate straight lines.

Q. The combined equation of the asymptotes of the hyperbola

2 x^{2} + 5 x y + 2 y^{2} + 4 x + 5 y = 0

Join BYJU'S Learning Program

2x2+3y2−5xy+5x−5y=0This is the equation of a

$2 x^{2} + 3 y^{2} - 5 x y + 5 x - 5 y = 0$
This is the equation of a