Consider the circles x2+(y-1)2=9,(x-1)2+y2=25. They are such that-

Question

Consider the circles x2+(y-1)2=9,(x-1)2+y2=25. They are such that- (A) each of these circles lies outside the other (B) one of these circles lies entirely inside the other (C) these circles touch each other (D) they intersect in two points

Tardigrade Admin · Accepted Answer

C1(0,1), r1=3 C2(1,0), r2=5 C1 C2=√2 |r1-r2|=2 ⇒ c1 c2<|r1-r2|

Q. Consider the circles $x^{2} + (y - 1)^{2} = 9, (x - 1)^{2} + y^{2} = 25$ . They are such that-

each of these circles lies outside the other

one of these circles lies entirely inside the other

these circles touch each other

they intersect in two points

$C_{1} (0, 1), r_{1} = 3$
$C_{2} (1, 0), r_{2} = 5$
$C_{1} C_{2} = 2$
$∣ r_{1} - r_{2} ∣ = 2$
$\Rightarrow c_{1} c_{2} < ∣ r_{1} - r_{2} ∣$

Q. Consider the circles x2+(y−1)2=9,(x−1)2+y2=25. They are such that-