Equations of the common tangents of the circles $$x2+y$$ $$2$$ –$$2x$$ –$$6y+9=0$$ and $$x2$$ $$+$$ $$y2$$ $$+$$ $$6x$$ – $$2y$$ $$+$$ $$1$$ $$=$$ $$0$$ $$areA)$$ x $$=$$ $$0$$ $$B)$$ y $$=$$ $$4$$ $$C)$$ $$3x$$ $$+4$$ y $$=10$$

Question

Equations of the common tangents of the circles $$x2+y$$ $$2$$ –$$2x$$ –$$6y+9=0$$ and $$x2$$ $$+$$ $$y2$$ $$+$$ $$6x$$ – $$2y$$ $$+$$ $$1$$ $$=$$ $$0$$ $$areA)$$ x $$=$$ $$0$$   $$B)$$ y $$=$$ $$4$$   $$C)$$ $$3x$$ $$+4$$ y $$=10$$

Infinity Learn · Accepted Answer

Equations of the given circles can be written as $$C1$$: (x$$ – $$1)2$$ $$+$$ $$(y$$ –$$3)2$$ $$=$$ $$1$$ having centre at $$(1$$, $$3) and radius $$1$$ and $$C2$$: (x$$ $$+$$ $$3)2$$ $$+$$ $$(y$$ –$$1)2$$ $$=$$ $$9$$ having centre at $$($$–$$3$$, $$1) and radius $$3$$.Both the circles clearly touch x $$=$$ $$0$$ and y $$=$$ $$4$$ Now        $$3$$×$$1+4$$×$$3$$−$$1032+42=1and$$         $$3($$−$$3)+4(1)$$−$$1032+42=3Shows$$ that both the circles touch $$3x$$ $$+$$ $$4y$$ $$=$$ $$10$$ also.

Equations of the common tangents of the circles $x^{2} + y^{2} - 2 x - 6 y + 9 = 0$ and $x^{2} + y^{2} + 6 x - 2 y + 1 = 0$ are
A) x = 0 B) y = 4 C) 3x +4 y =10

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Equations of the common tangents of the circles x2+y 2 –2x –6y+9=0 and x2 + y2 + 6x – 2y + 1 = 0 areA) x = 0 B) y = 4 C) 3x +4 y =10

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

Equations of the common tangents of the circles $x^{2} + y^{2} - 2 x - 6 y + 9 = 0$ and $x^{2} + y^{2} + 6 x - 2 y + 1 = 0$ are
A) x = 0 B) y = 4 C) 3x +4 y =10