If the equation $lambda x squared minus 5 x y plus 6 y squared plus x minus 3 y equals 0$ represents a pair of straight lines then their point of intersection is

chemistry-

The transformed equation of $x squared plus y squared equals r squared$ when the axes are rotated through an angle 36° is

>>> Given equation is $x 2 + y 2 = r 2 .$ After rotation

$>>> x = X cos 3 6^{\circ} - Y sin 3 6^{\circ}$ and $y = X sin 3 6^{o} + Y cos 3 6^{\circ}$

$∴ X 2 (cos^{2} 3 6^{o} + sin^{2} 3 6^{o}) + Y 2 (sin^{2} 3 6^{o} + cos^{2} 3 6^{o}) = r 2$

$>>> \Rightarrow X 2 + Y 2 = r 2$

The transformed equation of $x squared plus y squared equals r squared$ when the axes are rotated through an angle 36° is

>>> Given equation is $x 2 + y 2 = r 2 .$ After rotation

$>>> x = X cos 3 6^{\circ} - Y sin 3 6^{\circ}$ and $y = X sin 3 6^{o} + Y cos 3 6^{\circ}$

$∴ X 2 (cos^{2} 3 6^{o} + sin^{2} 3 6^{o}) + Y 2 (sin^{2} 3 6^{o} + cos^{2} 3 6^{o}) = r 2$

$>>> \Rightarrow X 2 + Y 2 = r 2$

maths-

When axes rotated an angle of $pi over 3$ the transformed form of $7 x squared plus 2 square root of 3 x y plus 9 y squared 8 equals 0$ is

maths-General

The transformed equation of $x squared over a squared minus y squared over b squared equals 1$ when the axes are rotated through an angle 90° is

$X equals y Y equals negative x$
>>> Therefore, the equation becomes $y squared over a squared minus x squared over b squared$ =1.

The transformed equation of $x squared over a squared minus y squared over b squared equals 1$ when the axes are rotated through an angle 90° is

$X equals y Y equals negative x$
>>> Therefore, the equation becomes $y squared over a squared minus x squared over b squared$ =1.

maths-

The arrangement of the following in ascending order of angle to eliminate xy term in the following equations
A) $2 x squared plus 5 x y plus 2 y squared plus 5 x plus 7 y plus 1 equals 0$
B) $2 x squared minus square root of 3 x y plus 3 y squared equals 9$
C) $9 x squared plus 2 square root of 3 x y end root plus 5 y squared equals 10$

maths-General

The angle of rotation of axes to remove xy term of the equation $x y equals c squared$ is

Angle of rotation will be $4 5 degrees.$

The angle of rotation of axes to remove xy term of the equation $x y equals c squared$ is

Angle of rotation will be $4 5 degrees.$

The angle of rotation of axes in order to eliminate xy term of the equation $x squared plus 2 square root of 3 x y minus y squared equals 2 a squared$ is

The Angle of rotation becomes $straight pi over 6$

The angle of rotation of axes in order to eliminate xy term of the equation $x squared plus 2 square root of 3 x y minus y squared equals 2 a squared$ is

The Angle of rotation becomes $straight pi over 6$

If the axes are rotated through an angle 45° in the anti-clockwise direction, the coordinates of $left parenthesis square root of 2 comma negative square root of 2 right parenthesis$ in the new system are

The point ( $square root of 2 comma negative square root of 2$ ) becomes (2,0) after rotation through 45 degrees in anti clockwise direction.

If the axes are rotated through an angle 45° in the anti-clockwise direction, the coordinates of $left parenthesis square root of 2 comma negative square root of 2 right parenthesis$ in the new system are

The point ( $square root of 2 comma negative square root of 2$ ) becomes (2,0) after rotation through 45 degrees in anti clockwise direction.

If the axes are rotated through an angle of 45° and the point p has new co-ordinates $left parenthesis 2 square root of 2 comma square root of 2 right parenthesis$ then original coordinates of p are

>>> Therefore, the original point is (3,1).

If the axes are rotated through an angle of 45° and the point p has new co-ordinates $left parenthesis 2 square root of 2 comma square root of 2 right parenthesis$ then original coordinates of p are

>>> Therefore, the original point is (3,1).

Assertion (A) : If the area of triangle formed by (0,0),(-1,2),(1,2) is 2 square units. Then the area triangle on shifting the origin to a point (2,3) is 2 units.
Reason (R):By the change of axes area does not change
Choose the correct answer

Both assertion and reason are correct and the reason is correct explanation of assertion.

Assertion (A) : If the area of triangle formed by (0,0),(-1,2),(1,2) is 2 square units. Then the area triangle on shifting the origin to a point (2,3) is 2 units.
Reason (R):By the change of axes area does not change
Choose the correct answer

Both assertion and reason are correct and the reason is correct explanation of assertion.

The point (4,1) undergoes the following successively
i) reflection about the line y=x
ii) translation through a distance 2 unit along the positive direction of y-axis. The final position of the point is

Therefore, the required point is (1,6).

The point (4,1) undergoes the following successively
i) reflection about the line y=x
ii) translation through a distance 2 unit along the positive direction of y-axis. The final position of the point is