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Find the equation of the circle with cen...

Find the equation of the circle with center at `(3,-1)` and which cuts off an intercept of length 6 from the line `2x-5y+18=0`

Text Solution

Verified by Experts

The correct Answer is:
`(x-3)^(2)+(y+1)^(2)=38`
Let the circle be as shown below.
`CM=(|2(3)-(5(-1)+18)|)/(sqrt(2^(2)+(-5)^(2)))=sqrt(29)`

`:. AC^(2)=AM^(2)+CM^(2)=9+29=38`
`:. ` Radius `=sqrt(38)`
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Find the equation of the circle whose centre is at (3,-1) and which cuts off a chord of length 6u n i t s on the line 2x-5y+18=0.

Find the equation of the circle whose centre is at (3,-1) and which cuts off a chord of length 6u n i t s on the line 2x-5y+18=0.

Knowledge Check

  • Find the equation of the circle which passes through the origin and cuts off intercepts -2 and 3 from the coordinate axes .

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    `x^(2) + y^(2) + 2x + 3y = 0
    B
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