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Show that the circles x^(2) +y^(2) -4x...

Show that the circles
`x^(2) +y^(2) -4x-6y-12=0` and
`5(x^(2)+y^(2))-8x - 14y - 32 = 0` touch each
other and find their point of contact.

Text Solution

Verified by Experts

The correct Answer is:
(i) (-1,-1) (ii) (11/5,-7/5)` (iii) `(1/5,3/5)` external
(iv) `(1/13,(-21)/13),5x+12y+19=0`
(v) `(5,1),4x-7y-13=0`
(iv) `(5,5),4x+3y-35=0`
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Knowledge Check

  • If the circle x^(2) + y^(2) + 2kx - 4y+1=0 and x^(2)+y(2)-8x-12 y + 43 = 0 " touch each other theb k ="

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