Question

find the problem very challenging ​

Answer 1

QUESTION :–

• Find the transformation of equation of x² + y² + 2x - 4y + 1 = 0 When the origin is shifted to the point (-1 , 2).

ANSWER :–

GIVEN :–

• Equation of curve => x² + y² + 2x - 4y + 1 = 0

• Origin shifted to the point ( -1 , 2).

TO FIND :–

• Shifted from of curve = ?

SOLUTION :–

$\\ \: { \huge{.}} \: { \bold{(x,y) \dashrightarrow \: old \: \: coordinate}}$

$\\ \: { \huge{.}} \: { \bold{(X,Y) \dashrightarrow \: new \: \: coordinate}}$

• Relation between old and new coordinate –

$\\ \implies { \bold{(x,y) = (X+ h, Y+ k)}}$

• So that –

$\\ \: { \huge{.}} \: { \bold{(h,k) = \: ( - 1,2)}}$

• So that –

$\\ \implies { \bold{(x,y) = (X - 1, Y+ 2)}}$

• Now put in equation –

$\\ \implies { \bold{ {x}^{2} + {y}^{2} + 2x - 4y + 1 = 0}}$

$\\ \implies { \bold{ {(X - 1)}^{2} + {(Y+ 2)}^{2} + 2(X - 1) - 4(Y+ 2) + 1 = 0}}$

$\\ \implies { \bold{ {X}^{2} + 1 - 2X + {Y}^{2} + 4 + 4Y+ 2X -2 - 4Y - 8+ 1 = 0}}$

$\\ \implies { \bold{ {X}^{2} + 1 + {Y}^{2} + 4 -2 - 8+ 1 = 0}}$

$\\ \implies { \bold{ {X}^{2} + {Y}^{2} + 5-10= 0}}$

$\\ \implies { \bold{ {X}^{2} + {Y}^{2} - 5= 0}}$

$\\ \implies \large{ \boxed{ \bold{ {X}^{2} + {Y}^{2} = 5}}}$