Answer to Question #294752 in Analytic Geometry for Denver

Question

How to find the coordinate of p and q if the circle cuts the x-axis at the points p and q in 2x^2 +2y^2 -8x +5y -10=0

Answer 1

Since the circle cuts the x-axis then $y=0$.

Substituting $y=0$ into the given equation of the circle, $2x^2 +2y^2 -8x +5y -10=0$, we have

$2x^2-8x-10=0\\ \Rightarrow x^2-4x-5=0\\ \Rightarrow (x-5)(x+1)=0\Rightarrow x=-1,5$

Thus, without loss of generality, the circle cuts the x-axis at P$(-1,0)$ and Q$(5,0)$