Login/Sign Up
What does the equation \[{{\left( x-a \right)}^{~2}}+{{\left( y-b \right)}^{~2}}~=\text{ }{{r}^{2}}\]become when the axes are transferred to parallel axes through the point (a-c, b)?
What does the equation \[{{\left( x-a \right)}^{~2}}+{{\left( y-b \right)}^{~2}}~=\text{ }{{r}^{2}}\]become when the axes are transferred to parallel axes through the point (a-c, b)?
Brief review of Cartesian System of Rectangular Coordinates | CBSE | Class 11 | Exercise 22.3 | Maths | RD Sharma
What does the equation \[{{\left( x-a \right)}^{~2}}+{{\left( y-b \right)}^{~2}}~=\text{ }{{r}^{2}}\]become when the axes are transferred to parallel axes through the point (a-c, b)?

Solution:

We have the equation:

\[{{\left( x-a \right)}^{~2}}+{{\left( y-b \right)}^{~2}}~=\text{ }{{r}^{2}}\]

The above-given equation (x – a)2 + (y – b)2 = r2 can be re-written into a new equation by replacing x by x – a + c and y by y – b, i.e. with the help of substitution of x by x + a and y by y + b.

$ {{\left( \left( x\text{ }+\text{ }a-c \right)-a \right)}^{2}}~+\text{ }{{\left( \left( y-b\text{ } \right)-b \right)}^{2}}~=\text{ }{{r}^{2}} $

$ {{\left( x-c \right)}^{2}}~+\text{ }{{y}^{2}}~=\text{ }{{r}^{2}} $

$ {{x}^{2}}~+\text{ }{{c}^{2}}-2cx\text{ }+\text{ }{{y}^{2}}~=\text{ }{{r}^{2}} $

$ {{x}^{2}}~+\text{ }{{y}^{2}}-2cx\text{ }=\text{ }{{r}^{2}}-{{c}^{2}} $

Hence, the transformed equation is  $ {{x}^{2}}~+\text{ }{{y}^{2}}-2cx\text{ }=\text{ }{{r}^{2}}-{{c}^{2}} $

i

More Material