If the circles x2 + y2 - 16x-20y + 164 = r2 and (x-4)2 + (y - 7)2 = 36 intersect at two distinct points, then:

Question

If the circles x2 + y2 - 16x-20y + 164 = r2 and (x-4)2 + (y - 7)2 = 36 intersect at two distinct points, then: (A) 0 < r < 1 (B) 1 < r < 11 (C) r > 11 (D) r = 11

Tardigrade Admin · Accepted Answer

x2 + y2 - 16x - 20y + 164 = r2 A(8,10), R1 = r (x - 4)2 + (y - 7)2 = 36 B(4,7), R2 = 6 |R1 - R2| < AB < R1 + R2 ⇒ 1 < r < 11

Q. If the circles $x^{2} + y^{2} - 16 x - 20 y + 164 = r^{2}$ and $(x - 4)^{2} + (y - 7)^{2} = 36$ intersect at two distinct points, then:

$0 < r < 1$

$1 < r < 11$

$r > 11$

$r = 11$

$x^{2} + y^{2} - 16 x - 20 y + 164 = r^{2}$
$A (8, 10), R_{1} = r$
$(x - 4)^{2} + (y - 7)^{2} = 36$
$B (4, 7), R_{2} = 6$
$∣ R_{1} - R_{2} ∣ < A B < R_{1} + R_{2}$
$\Rightarrow 1 < r < 11$

Q. If the circles x2+y2−16x−20y+164=r2 and (x−4)2+(y−7)2=36 intersect at two distinct points, then:

0<r<1

1<r<11

r>11

r=11