Determine the equation of the curves `(a) ax + by= c, (b)x^2+y^2=r^2, (c) x^2+ 9y^2=1` with respect to the change of origin to `(3, 0)`

Find the equation of the curve x^2 + y^2 - 3x + 5y - 8 = 0 when the origin is shifted to (1, 2) without changing the direction of axes.

If the transformed equation of a curve is 3X^(2) + XY - Y^(2)- 7X + Y +7=0 when the axes are translated to the point (1,2), then the original equation of the curve is 3x^(2) + xy - y^(2) -ax + by+c=0 , then the ascending order of a,b,c is

Let the equation of the curve x^(2)-xy-y^(2)=11 be transformed to ax^(2)-by^(2)+3x+cy+dxy=e upon shifting the origin to (1,-1) then a^(2)+b^(2)+c^(2)=

If the transformed equation of curve is 3x^(2) + xy - y^(2) - 7x + y + 7 = 0 when the axes are translated to the point (1,2) then the original equation of curve is

Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x^2-9y^2 +30 = 0 (b) 4x^2-9y^2-30 = 0 (c) 9x^2-4y^2-30=0 (d) none of these

Find the equation of the curve 2x^(2)+y^(2)-3x+5y-8=0 when the origin is transferred to the point (-1, 2) without changing the direction of axes.

Find the equation of the curve 2x^(2)+y^(2)-3x+5y-8=0 when the origin is transferred to the point (-1, 2) without changing the direction of axes.

Find the equation of the curve 2x^(2)+y^(2)-3x+5y-8=0 when the origin is transferred to the point (-1, 2) without changing the direction of axes.

If the transformed equation of a curve is X^(2) + 3XY - 2Y^(2) + 17X - 7Y - 11 = 0 when the axes are translated to the point (2,3) then find the original equation of the curve.