The intercepts made by the circle `x^2+y^2-5x-13y-14=0` on the x- axis and the y-axis are :

Explanation

Let points of intersection on the x-axis are `(x_1,0) and (x_2,0) `and

points of intersection on y-axis is `(0,y_1) and (0,y_2)`.

Then, `|x_2-x_1|` and `|y_2-y_1|` will be the x-intercepts and y-intercepts.

Now, when `y = 0`, equation of circle becomes,

`x^2-5x-14 = 0`

Here, `x_1+x_2= 5` and `x_1x_2 = -14`

So, `(x_2-x_1)^2 = (x_1+x_2)^2-4(x_1)(x_2)`

`(x_2-x_1)^2 = 25-(-56) = 81`

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