The equation of a curve referred to a given system of axes is `3x^2+2x y+3y^2=10.` Find its equation if the axes are rotated through an angle `45^0` ,

Question

The equation of a curve referred to a given system of axes is `3x^2+2x y+3y^2=10.` Find its equation if the axes are rotated through an angle `45^0` ,

The equation of a curve referred to a given system of axes is `3x^2+2x y+3y^2=10.` Find its equation if the axes are rotated through an angle `45^0` , the origin remaining unchanged.

Monjur Alahi

4 views

2025-01-04 04:42

1 Answers

Related Questions

Find the equation of a curve passing through the origin given that the slope of the tangent to the curve at any point (x, y) is equal to the sum of th

2 Answers 4 Views

Find the equation of the curve passing through origin if the slope of the tangent to the curve at any point `(x ,y)i s` equal to the square of the dif

2 Answers 9 Views

The plane `4x+7y+4z+81=0` is rotated through a right angle about its line of intersection with the plane `5x+3y+10 z=25.` The equation of the plane in

2 Answers 4 Views

The plane denoted by `P_(1) : 4x+7y+4z+81=0` is rotated through a right angle about its line of intersection with the plane `P_(2) : 5x+3y+ 10 z = 25`

2 Answers 5 Views

The equation of curve referred to the new axes, axes retaining their directions, and origin `(4,5)` is `X^2+Y^2=36` . Find the equation referred to th

2 Answers 5 Views

The axes are rotated through an angle `pi//3` in the anticlockwise direction with respect to `(0,0)`. Find the coordinates of point `(4,2)` (w.r.t. ol

2 Answers 4 Views

If `theta` is an angle by which axes are rotated about origin and equation `ax^2+2hxy+by^2=0` does not contain xy term in the new system, then prove t

2 Answers 6 Views

Given the equation `4x^2+2sqrt(3)x y+2y^2=1` . Through what angle should the axes be rotated so that the term `x y` is removed from the transformed eq

2 Answers 4 Views

Find the equation of normal to the parabola `y=x^2-x-1` which has equal intercept on the axes. Also find the point where this normal meets the curve a

2 Answers 5 Views

Find the equation of tangents of the following curves at the given points: (i) Curve`x^(2) = 25` at point (3, 4) (ii) Curve `y = 2x^(3) + 2x^(2) - 8x+

2 Answers 5 Views

Salim Ahmed Kawsar · Accepted Answer · 2023-02-05T15:29:48+06:00

We have
`x=Xcostheta-Ysin theta`
`=X cos theta 45^@-Ysin45^@=(X)/(sqrt2)+(Y)/(sqrt2)`
`y=X sintheta+Ycostheta`
`=X sintheta 45^@-Ycos45^@=(X)/(sqrt2)+(Y)/(sqrt2)`
Hence, the equation `3x^2+2xy+3y^2=10` transforms to
`3((X)/(sqrt2)-(Y)/(sqrt2))^2+2((X)/(sqrt2)-(Y)/(sqrt2))((X)/(sqrt2)+(Y)/(sqrt2))+3((X)/(sqrt2)+(Y)/(sqrt2))^2=10`
or `2X^2+Y^2=5`