The equation of the circle which touches the axes of the coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is $x^{2} + y^{2} - 2 c x - 2 c y + c^{2} = 0,$
where $c,$ is

Question

The equation of the circle which touches the axes of the coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is $x^{2} + y^{2} - 2 c x - 2 c y + c^{2} = 0,$

where $c,$ is

Infinity Learn · Accepted Answer

The equation of a circle touching the coordinate axes is                   $$(x$$−$$c)2+(y$$−$$c)2=c2This$$ touches $$x3+y4=1$$, i.e. $$4x+3y$$−$$12=0$$∴ $$4c+3c$$−$$1242+32=c$$⇒|$$7c$$−$$12$$|$$=5c$$⇒$$c=6$$,$$1Thus$$, the equation of the required circle is    $$x2+y2$$−$$2cx$$−$$2cy+c2=0$$, where $$c=1$$,$$6$$

The equation of the circle which touches the axes of the coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is $x^{2} + y^{2} - 2 c x - 2 c y + c^{2} = 0,$
where $c,$ is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The equation of the circle which touches the axes of the coordinates and the line x3+y4=1and whose centre lies in the first quadrant isx2 + y2 - 2cx -2cy + c2 = 0,where c, is

Remember concepts with our Masterclasses.

Ready to Test Your Skills?

free study material

The equation of the circle which touches the axes of the coordinates and the line $\frac{x}{3} + \frac{y}{4} = 1$ and whose centre lies in the first quadrant is $x^{2} + y^{2} - 2 c x - 2 c y + c^{2} = 0,$
where $c,$ is