Question

When the axes are translated to the point $(1,\frac{1}{2})$, the equation $5x^2+4xy+8y^2-12x-12y=0$

transforms to

• A. $5X^2+4XY+8Y^2=9$
• B. $2X^2+3XY+4Y^2=0$
• C. $X^2+2Y^2-3Y=0$
• D. $X^2-7XY+8Y^2=0$

Answer 1

The correct option is A $5X^2+4XY+8Y^2=9$

$\Rightarrow$Let the point $(x,y)$ on the line changes to $(X,Y)$ on shifting the origin to $(h,k)$.

Then, $x=X+h,y=Y+k$

$\Rightarrow x=X+1,y=Y+\frac{1}{2}$

So, the equation transform to ...(substitute the values of x and y in the given equation of question)

$\Rightarrow 5(X+1{)}^2+4(X+1)(Y+\frac{1}{2})+8{(Y+\frac{1}{2})}^2-12(X+1)-12(Y+\frac{1}{2})=0$

$\Rightarrow 5X^2+4XY+8Y^2-9=0$

So, the transformed equation is $5X^2+4XY+8Y^2=9$.