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The straight line x/a+y/b=1 cuts the ...

The straight line `x/a+y/b=1` cuts the coordinate axes at `A` and `B` . Find the equation of the circle passing through `O(0,0),Aa n dBdot`

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To find the equation of the circle passing through the points O(0,0), A(a,0), and B(0,b), we can follow these steps: ### Step 1: Identify the points A and B The line given is \( \frac{x}{a} + \frac{y}{b} = 1 \). - The point A is where the line intersects the x-axis. At this point, \( y = 0 \): \[ \frac{x}{a} + \frac{0}{b} = 1 \implies x = a \implies A(a, 0) \] ...
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Knowledge Check

  • The straight line x + 2y = 1 meets the coordinate axes at A and B. A circle is drawn through A,B and the origin. Then, the sum of perpendicular distances from A and B on the tangent to the circle at the origin is

    A
    `2sqrt5`
    B
    `(sqrt5)/(4)`
    C
    `4sqrt5`
    D
    `(sqrt5)/(2)`
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