The common tangent to the circles x2 + y2 = 4 and x2 + y2 + 6x + 8y - 24 = 0 also passes through the point :

Question

The common tangent to the circles x2 + y2 = 4 and x2 + y2 + 6x + 8y - 24 = 0 also passes through the point : (A) (-4, 6) (B) (6, -2) (C) (-6, 4) (D) (4, -2)

Tardigrade Admin · Accepted Answer

Circle touches internally C1(0, 0); r1 = 2 C2: (-3, -4); r2 = 7 C1C2 = |r1 - r2| S1 - S2 = 0 ⇒ eqn. of common tangent 6x + 8y - 20 = 0 3x + 4y = 10 (6, -2) satisfy it

Q. The common tangent to the circles $x^{2} + y^{2} = 4$ and $x^{2} + y^{2} + 6 x + 8 y - 24 = 0$ also passes through the point :

(-4, 6)

(6, -2)

(-6, 4)

(4, -2)

Circle touches internally
$C_{1} (0, 0); r_{1} = 2$
$C_{2} : (- 3, - 4); r_{2} = 7$
$C_{1} C_{2} = ∣ r_{1} - r_{2} ∣$
$S_{1} - S_{2} = 0 \Rightarrow$ eqn. of common tangent
$6 x + 8 y - 20 = 0$
$3 x + 4 y = 10$
$(6, - 2)$ satisfy it

Q. The common tangent to the circles x2+y2=4 and x2+y2+6x+8y−24=0 also passes through the point :