Question

Find the value of x-intercept made by the circle $x^2+y^2-14x+9y+45=0$

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Answer 1

some circles cut the x-axis as shown in the figure.

we want to find the value of $x^2-x$.

we will first find $x^2$ and $x^1$ by putting y=0 in the equation of the circle [At $x^1$ and $x^2$ the y -co-ordinate is

zero].

$\Rightarrow x^2-14x+45=0$

$\Rightarrow (x-9)(x-5)=0$

$\Rightarrow x=9or5$

$\Rightarrow x_2=9and{x}_1=5$

$\Rightarrow x_2-x_1=9-5=4$

we can do this by using formula also.

The x-intercept made by the circle

$x^2+y^2+2gx+2fy+c=0$ is given by $2\sqrt{g^2-c}$

$\Rightarrow 2\sqrt{(-7{)}^2-45}=2\times 2=4$