Question

If. a circle C passing through (4, 0) touches the circle x² + y²
+ 4x - 6y – 12 = 0 externally: (1, -1), then the radius of the circle C is:
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Answer 1

Answer:

Step-by-step explanation:

x  2 +y  2 +4x−6y−12=0

Equation of tangent at (1,−1)

x−y+2(x+1)−3(y−1)−12=0

3x−4y−7=0

∴ Equation of circle is

(x  2  +y  2  +4x−6y−12)+λ(3x−4y−7)=0

It passes through (4,0):

(16+16−12)+λ(12−7)=0

⇒20+λ(5)=0

⇒λ=−4

∴(x  2 +y  2 +4x−6y−12)−4(3x−4y−7)=0

or x  2  +y  2  −8x+10y+16=0

Radius =  16+25−16

=5.