Question

1. For the circle x2 + y2 - 4x + 4y - 42 = 0.

1. Find the centre and radius.
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Answer 1

Answer:)

The equation of any straight line passing through point (4,2) is

y−2=m(x−4)⟶(1)

From (1) is target to the given circle provided the length of the perpendicular from center of given circle to (1) is equal to radius of the circle

x

2

+y

2

−4x−4y+4=0

2g=−4⇒g=−2

2f=−4f=−2

Center =(−g,−f)=(2,2)

r=

g

2

+f

2

−c

=

4+4+4

=2m=

x−4

y−2

Slope of tangent x−4=0 x=4 Equation of tangent (i) x=4

I hope this helps to you ☺️