MyQuestionIcon

1

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Distinguishing between Conics from General Equation and Eccentricity

For the value...

Question

For the value of $λ$ obtained in above question, if $L_{1} = 0 a n d L_{2} = 0$ are the lines denoted by the given equation, then the product of the abscissa and ordinate of their point of intersection is

A

18

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

B

28

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

C

35

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

D

25

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

Open in App

Solution

The correct option is B 35
The equation of $2^{n d}$ degree is
$2 x^{2} - 10 x y + 12 y^{2} + 5 x - 16 y - 3 = 0$
$\Rightarrow (2 x - 4 y + 6) = 0 a n d x - 3 y - \frac{1}{2} = 0$
their point of intersection is $(- 10, - \frac{7}{2})$

Suggest Corrections

thumbs-up

0

Similar questions

Consider a general equation of degree

2

λ x^{2} - 10 x y + 12 y^{2} + 5 x - 16 y - 3 = 0

For the value of

λ

obtained for the given equation to be a pair of straight lines, if

L_{1} = 0

L_{2} = 0

are the lines denoted by the given line pair then the product of the abscissa and ordinate of their point of intersection is

Q. Consider a general equation of degree

2

λ x^{2} - 10 x y + 12 y^{2} + 5 x - 16 y - 3 = 0

For the value of

λ

obtained for the given equation to be a pair of straight lines, if

θ

is the acute angle between

L_{1} = 0

L_{2} = 0

θ

lies in the interval

Q. If a circle passes through the points of intersection of the co-ordinate axes with the lines

λ x - y + 1 = 0

x - 2 y + 3 = 0,

then the value of

λ

Q. Assertion :The straight line

(sin θ + \sqrt{3} cos θ) x + (\sqrt{3} sin θ - cos θ) y + (5 sin θ - 7 cos θ) = 0

passes through the point of intersection of the lines

x + \sqrt{3} y + 5 = 0

\sqrt{3} x - y - 7 = 0

for all values of

θ

θ = \frac{n π}{2}

n

is an integer. Reason:

L_{1} + λ L_{2} = 0

represents the equation of a line through the points of intersection of the lines

L_{1} = 0

L_{2} = 0

for all non-zero finite values of

λ

.

Q. For what value of

λ

does the equation

12 x^{2} - 10 x y + 2 y^{2} + 11 x - 5 y + λ = 0

represent a pair of straight lines? Find their equations, point of intersection, acute angle between them and pair of angle bisector.

View More

Join BYJU'S Learning Program

similar_icon

Related Videos

lock

Defining Conics

MATHEMATICS

Watch in App

explore_more_icon

Explore more

Distinguishing between Conics from General Equation and Eccentricity

Standard XII Mathematics

Join BYJU'S Learning Program

CrossIcon