Let $$r1$$ and $$r2$$ be the radii of the largest and smallest circles, respectively, which pass through the point $$($$–$$4$$, $$1)$$ and having their centers on the circumference of the circle $$x2+y2+2x+4y-4=0$$. If $$r1r2=a+b2$$, then $$a+b$$ is equal to :

Question

Let $$r1$$ and $$r2$$ be the radii of the largest and smallest circles, respectively, which pass through the point $$($$–$$4$$, $$1)$$ and having their centers on the circumference of the circle $$x2+y2+2x+4y-4=0$$. If $$r1r2=a+b2$$, then $$a+b$$ is equal to :

Infinity Learn · Accepted Answer

$$r2=OP+r$$ $$r1=OP-r$$ $$r=9+9$$ $$r=3$$   $$OP=32$$ $$r1r2=OP+rOP-r=32+332-3$$                       $$=2+12-1$$       $$a+b2=3+22$$              $$a+b=2$$

Let $r_{1}$ and $r_{2}$ be the radii of the largest and smallest circles, respectively, which pass through the point (–4, 1) and having their centers on the circumference of the circle $x^{2} + y^{2} + 2 x + 4 y - 4 = 0 .$ If $\frac{r_{1}}{r_{2}} = a + b \sqrt{2}$ , then $a + b$ is equal to :

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Let r1 and r2 be the radii of the largest and smallest circles, respectively, which pass through the point (–4, 1) and having their centers on the circumference of the circle x2+y2+2x+4y-4=0. If r1r2=a+b2, then a+b is equal to :

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Ready to Test Your Skills?

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Let $r_{1}$ and $r_{2}$ be the radii of the largest and smallest circles, respectively, which pass through the point (–4, 1) and having their centers on the circumference of the circle $x^{2} + y^{2} + 2 x + 4 y - 4 = 0 .$ If $\frac{r_{1}}{r_{2}} = a + b \sqrt{2}$ , then $a + b$ is equal to :