What does the equation `2x^2+4x y-5y^2+20 x-22 y-14=0` become when referred to the rectangular axes through the point `(-2,-3)` , the new axes being inclined at an angle at `45^0` with the old axes?

Write the equations for the x-and y-axes.

If a circle passes through the points where the lines 3kx- 2y-1 = 0 and 4x-3y + 2 = 0 meet the coordinate axes then k=

Find the equation of the lines passing through the point of intersection lines 4x-y+3=0 and 5x+2y+7=0 Parallel to x-y+5=0

Find the equation of the lines passing through the point of intersection lines 4x-y+3=0 and 5x+2y+7=0 through the point (-1,2)

The circle x^2+y^2-6x-10 y+k=0 does not touch or intersect the coordinate axes, and the point (1, 4) is inside the circle. Find the range of value of kdot

The equation of a straight line passing through the point (2, 3) and inclined at an angle of tan^(-1)(1/2) with the line y+2x=5 y=3 (b) x=2 3x+4y-18=0 (d) 4x+3y-17=0

Let S be the circle in the x y -plane defined by the equation x^2+y^2=4. (For Ques. No 15 and 16) Let P be a point on the circle S with both coordinates being positive. Let the tangent to S at P intersect the coordinate axes at the points M and N . Then, the mid-point of the line segment M N must lie on the curve (a) (x+y)^2=3x y (b) x^(2//3)+y^(2//3)=2^(4//3) (c) x^2+y^2=2x y (d) x^2+y^2=x^2y^2

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 the original axes.