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The circle x^(2) +y^(2)-8x=0 " and hyper...

The circle `x^(2) +y^(2)-8x=0 " and hyperbola " (x^(2))/(a^(2))-(y^(2))/(b^(2))=1` intersect at the points A and B.
Equation of the circle with AB as its diameter is

A

`2x-5sqrt(y)-20=0`

B

`2x-5sqrt(y)+4=0`

C

`3x-4y+8=0`

D

`4x-3y+4=0`

Text Solution

Verified by Experts

Equation of tangent to hyperbola having slope m is
`y=mx+sqrt(9m^(2)-4) " …(i)" `
Equation of tangent to circle is
`y=m(x-4)+sqrt(16m^(2)+16) " …(ii)" `
Eqs. (i) and (ii) will be identical for`m=(2)/(sqrt(5))` satisfy.
` therefore ` Equation of common tangent is `2x-sqrt(5)y+4=0.`
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