The equation of the line concurrent with the pair of lines $3 x y minus 2 y squared minus 7 x plus y plus 3 equals 0$ is

>>>The point of intersection of the pair of straight lines x² – 5xy + 6y² + x – 3y = 0 is (-3, -1)

maths-

The point of intersection of the perpendicular lines $a x squared plus 3 x y minus 2 y squared minus 5 x plus 5 y plus c equals 0$ is

maths-General

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