HSC Arts (English Medium) इयत्ता ११ वी - Maharashtra State Board Question Bank Solutions for Mathematics and Statistics

Prove the following:

`tan^3x/(1 + tan^2x) + cot^3x/(1 + cot^2x)` = secx cosecx − 2sinx cosx 

If A(1, 3) and B(2, 1) are points, find the equation of the locus of point P such that PA = PB.

A(−5, 2) and B(4, 1). Find the equation of the locus of point P, which is equidistant from A and B

If A(2, 0) and B(0, 3) are two points, find the equation of the locus of point P such that AP = 2BP.

If A(4, 1) and B(5, 4), find the equation of the locus of point P if PA² = 3PB² 

A(2, 4) and B(5, 8), find the equation of the locus of point P such that PA² − PB² = 13

A(1, 6) and B(3, 5), find the equation of the locus of point P such that segment AB subtends right angle at P. (∠APB = 90°)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new co-ordinates of the point A(1, 3)

If the origin is shifted to the point O′(2, 3), the axes remaining parallel to the original axes, find the new coordinates of the point B(2, 5)

If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point C(5, 4)

If the origin is shifted to the point O′(1, 3) the axes remaining parallel to the original axes, find the old coordinates of the point D(3, 3)

If the co-ordinates A(5, 14) change to B(8, 3) by shift of origin, find the co-ordinates of the point where the origin is shifted

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

3x − y + 2 = 0

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

x² + y² – 3x = 7

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

xy − 2x − 2y + 4 = 0

Obtain the new equation of the following loci if the origin is shifted to the point O'(2, 2), the direction of axes remaining the same:

y² − 4x − 4y + 12 = 0

Find the equation of the circle with centre at origin and radius 4.

Find the equation of the circle with centre at (−3, −2) and radius 6.

Find the equation of the circle with centre at (2, −3) and radius 5.

Find the equation of the circle with centre at (−3, −3) passing through the point (−3, −6)