Let r1 and r2 be the radii of the largest and smallest circles, respectively, which pass through the point (-4,1) and having their centres on the circumference of the circle x2+y2+2 x+4 y-4=0. If (r1/r2)=a+b √2, 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 centres on the circumference of the circle x2+y2+2 x+4 y-4=0. If (r1/r2)=a+b √2, then a+b is equal to : (A) 3 (B) 11 (C) 5 (D) 7

Tardigrade Admin · Accepted Answer

<img class="img-fluid question-image" alt="image" src="https://cdn.tardigrade.in/img/question/mathematics/ae74bf468d56b68a59ab19d4bbb99925-.png" /> Centre of smallest circle is A Centre of largest circle is B r2=|C P-C A|=3 √2-3 r1=C P+C B=3 √2+3 (r1/r2)=(3 √2+3/3 √2-3)=((3 √2+3)2/9) =(√2+1)2=3+2 √2 a=3, b=2

Q. 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 centres on the circumference of the circle $x^{2} + y^{2} + 2 x + 4 y - 4 = 0$ . If $\frac{r _{1}}{r _{2}} = a + b 2$ , then $a + b$ is equal to :

3

11

5

7

Centre of smallest circle is $A$
Centre of largest circle is $B$
$r_{2} = ∣ CP - C A ∣ = 32 - 3$
$r_{1} = CP + CB = 32 + 3$
$\frac{r _{1}}{r _{2}} = \frac{3 2 + 3}{3 2 - 3} = \frac{( 3 2 + 3 ) ^{2}}{9}$
$= (2 + 1)^{2} = 3 + 22$
$a = 3, b = 2$

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

3

11

5

7

Centre of smallest circle is A Centre of largest circle is B r2​=∣CP−CA∣=32​−3 r1​=CP+CB=32​+3 r2​r1​​=32​−332​+3​=9(32​+3)2​ =(2​+1)2=3+22​ a=3,b=2

Q. 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 centres on the circumference of the circle $x^{2} + y^{2} + 2 x + 4 y - 4 = 0$ . If $\frac{r _{1}}{r _{2}} = a + b 2$ , then $a + b$ is equal to :

Centre of smallest circle is $A$
Centre of largest circle is $B$
$r_{2} = ∣ CP - C A ∣ = 32 - 3$
$r_{1} = CP + CB = 32 + 3$
$\frac{r _{1}}{r _{2}} = \frac{3 2 + 3}{3 2 - 3} = \frac{( 3 2 + 3 ) ^{2}}{9}$
$= (2 + 1)^{2} = 3 + 22$
$a = 3, b = 2$