1.1 – N – Analytical Geometry – II Exercise Problems

\[\underline{PART\ -\ A}\]

1.  Find the equation of the circle with centre (1, -2) and radius 5 units.

2.     Find the centre and radius of the circle  x2  +   y2 +  10x  +  8y  +  5 = 0 .

\[3.\ Find\ the\ centre\ and\ radius\ of\ the\ circle\ x^2\ +\ y^2\ +\ 4\ x\ +\ 4\ y\ -\ 1\ =\ 0\ \hspace{5cm}\]
\[4.\ Show\ that\ the\ circles\ x^2\ +\ y^2\ -\ 2\ x\ +\ 4\ y\ -\ 3\ =\ 0\ and\ \hspace{7cm}\]\[x^2\ +\ y^2\ -\ 2\ x\ +\ 4\ y\ +\ 5\ =\ 0\ are\ concentric\ circles\ \hspace{5cm}\]
\[\underline{PART\ -\ B}\]
\[5.\ Show\ that\ 2\ x\ +\ 3\ y\ +\ 9\ =\ 0\ is\ a\ diameter\ of\ the\ circle\ x^2\ +\ y^2\ -\ 6\ x\ +\ 10\ y\ -\ 1\ =\ 0\ \hspace{5cm}\]
\[6.\ Find\ the\ equation\ of\ the\ circle\ passing\ through\ the\ point\ (1,1)\ and\ \hspace{7cm}\]\[concentric\ to\ the\ circle\ x^2\ +\ y^2\ +\ 4\ x\ +\ 6\ y\ -\ 15\ =\ 0\ \hspace{5cm}\]
\[7.\ Find\ the\ equation\ of\ the\ circle\ concentric\ with\ the\ circle\ x^2\ +\ y^2\ -\ 6\ x\ +\ 10\ y\ -\ 1\ =\ 0\ \hspace{7cm}\]\[and\ passing\ through\ the\ point\ (1,1)\ \hspace{5cm}\]
\[8.\ Find\ the\ equation\ of\ the\ circle\ concentric\ with\ the\ circle\ x^2\ +\ y^2\ +\ 8\ x\ -\ 4\ y\ -\ 23\ =\ 0\ \hspace{7cm}\]\[and\ having\ radius\ 3\ units\ \hspace{5cm}\]
\[\underline{PART\ -\ C}\]

9.    Find the equation of the circle passing through the point  A (2, 3) and having its centre at C ( 4 , 1).

\[10.\ Find\ the\ equation\ of\ the\ circle\ passing\ through\ the\ point\ (-7.1)\ \hspace{7cm}\]\[and\ having\ its\ centre\ at\ (-4,-3)\ \hspace{5cm}\]
\[11.\ Find\ the\ equation\ of\ the\ circle,\ twp\ of\ whose\ diameters\ are\ 2\ x\ -\ 3\ y\ +\ 1\ =\ 0\ and\ \hspace{7cm}\]\[x\ +\ 2\ y\ -\ 17\ =\ 0\ and\ its\ radius\ is\ 8\ units\ \hspace{5cm}\]

12.     Prove that the circles  x2  +   y2  – 8x  + 6y – 23 = 0  and x2  +   y2  – 2x  – 5y + 16 = 0 cut orthogonally .

\[13.\ Show\ that\ the\ circles\ x^2 + y^2 + 2x – 8 = 0\ and\ x^2 + y^2 – 6x + 6y -46 = 0\ touch\ each\ other.\ \hspace10cm\]

14. Prove that the circles  x2  +   y2   – 2x  +  6y + 6= 0 and  x2  +   y2   – 5x  + 6y + 15 = 0 touch  each other. 

\[15.\ Prove\ that\ the\ circles\ x^2\ +\ y^2\ -\ 10\ x\ -\ 24\ y\ +\ 120\ =\ 0\ and\ \hspace{7cm}\]\[x^2\ +\ y^2\ =\ 400\ touch\ each\ other\ \hspace{5cm}\]
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