If the pair of straight lines a x2-2 h x y-b y2-0 is rotated about the origin through 90- then the equations in the new position isA- a x2-2 h x y-b y2-0B- a x2-2 h x y-b y2-0C- b x2-2 h x y-a y2-0D- b x2-2 h x y-a y2-0

The correct option is D bx^2 2hxy + ay^2 = 0When the axes rotated about 90° x=Y and y= X nbsp; hence putting the respective values in the above equation, w ...

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

Byju's Answer

Standard XII

Mathematics

Pair of Lines

If the pair o...

Question

If the pair of straight lines $a x^{2} + 2 h x y + b y^{2} = 0$ is rotated about the origin through $90^{\circ},$ then the equations in the new position is

a x^{2} - 2 h x y + b y^{2} = 0

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

a x^{2} + 2 h x y - b y^{2} = 0

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

b x^{2} + 2 h x y + a y^{2} = 0

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

b x^{2} - 2 h x y + a y^{2} = 0

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

Open in App

Solution

The correct option is D $b x^{2} - 2 h x y + a y^{2} = 0$
When the axes rotated about $90 °$
$x = Y$ and $y = - X$
hence putting the respective values in the above equation, we get
$b X^{2} - 2 h X Y + a Y^{2} = 0$
hence the equation will be
$b x^{2} - 2 h x y + a y^{2} = 0$

Suggest Corrections

Similar questions

Q. If the pair of straight lines

a x^{2} + 2 h x y + b y^{2} = 0

is rotated about the origin through

90^{\circ},

then the equations in the new position is

Q. If the pair of straight lines

a x^{2} + 2 h x y - a y^{2} = 0

and

b x^{2} + 2 g x y - b y^{2} = 0

be such that each bisect the angle between the other, then

Q. Show that the equation

b x^{3} - 2 h x y + a y^{2} = 0

represents a pair of straight lines which are at right angles to the pair given by the equation

a x^{2} + 2 h x y + b y^{2} = 0

Q. If the pair of line given by

a x^{2} + 2 h x y + b y^{2} = 0

are rotated through origin about

90^{\circ}

, then find combined equation of their equation in the new position.

Q. If the equation

a x^{2} + 2 h x y + b y^{2} + 2 g x + 2 f y + c = 0

represent a pair of straight lines, then prove that the equation to the third pair of straight lines passing through the points where these meet the axis is

a x^{2} - 2 h x y + b y^{2} + 2 g x + 2 f y + c + \frac{4 f g}{c} x y = 0

Join BYJU'S Learning Program

If the pair of straight lines ax2+2hxy+by2=0 is rotated about the origin through 90∘, then the equations in the new position is

The correct option is D bx2−2hxy+ay2=0When the axes rotated about 90° x=Y and y=−X hence putting the respective values in the above equation, we get bX2−2hXY+aY2=0 hence the equation will be bx2−2hxy+ay2=0

If the pair of straight lines $a x^{2} + 2 h x y + b y^{2} = 0$ is rotated about the origin through $90^{\circ},$ then the equations in the new position is

The correct option is D $b x^{2} - 2 h x y + a y^{2} = 0$
When the axes rotated about $90 °$
$x = Y$ and $y = - X$
hence putting the respective values in the above equation, we get
$b X^{2} - 2 h X Y + a Y^{2} = 0$
hence the equation will be
$b x^{2} - 2 h x y + a y^{2} = 0$