Question

The equation of a circle with centre $( - 4,3 )$ and touching the circle $x ^ { 2 } + y ^ { 2 } = 1$, is.

• A. $x ^ { 2 } + y ^ { 2 } + 8 x - 6 y + 9 = 0$
• B. $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y - 11 = 0$
• C. $x ^ { 2 } + y ^ { 2 } + 8 x + 6 y - 9 = 0$
• D. None of these

Answer 1

Answer: (A)

$x ^ { 2 } + y ^ { 2 } + 8 x - 6 y + 9 = 0$

Answer 2

Centre is $( - 4,3 )$

Radius = Distance between centres – Radius of other circle $= 5 - 1 = 4$

Hence equation of circle is $x ^ { 2 } + y ^ { 2 } + 8 x - 6 y + 9 = 0$.

Trick : Only option (1) has centre (–4, 3).