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…

Question

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+2x+4y-4=0. If r_1r_2=a+b√2, then a+b is equal to:

MARKS Content Team · Accepted Answer

Correct answer: (C) 5. We have, x^2+y^2+2x+4y-4=0 ⇒x^2+2x+1+y^2+4y+4=9 ⇒x+1^2+y+2^2=3^2 Centre≡-1,-2 CP=√(-4+1^2+1+2^2)=3√2 Centre of smallest circle is A Centre of largest circle is B. r_2=|CP-CA|=3√2-3 r_1=CP+CB=3√2+3 Hence, r_1r_2=(3√2+3)/(3√2-3)=((3√2+3)^2)/9 ⇒r_1r_2=(√2+1)^2=3+2√2 Hence, a=3, b=2 a+b=5

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 $\frac{r_{1}}{r_{2}} = a + b \sqrt{2},$ then $a + b$ is equal to:

Solution

Relevant Questions

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 r1r2=a+b2, then a+b is equal to:

Solution

Relevant Questions

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 $\frac{r_{1}}{r_{2}} = a + b \sqrt{2},$ then $a + b$ is equal to: