1.

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

Answer» 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`
`|x_2-x_1| = 9`
So, x-intercept is `9`.
Now, when `x = 0`, equation of circle becomes,
`y^2-13y-14 = 0`
Here, `y_1+y_2 = 5 and y_1y_2 = -14`
So, `(y_2-y_1)^2 = (y_1+y_2)^2-4y_1y_2`
`(y_2-y_1)^2 = 169-4(-14) = 225`
`|y_2-y_1| = 15`
So, y-intercept is `15`.


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