Question

In how many points do the graphs of the equations $x^2+y^2=25$ and $y^2=4x$ intersect?

• A. 0
• B. 1
• C. 2
• D. 3
• E. 4

Answer 1

Answer: (C)

2

Given equations are $x^2+y^2=25$ and $y^2=4x$
By substituting $y^2=4x$ in $x^2+y^2=25$, we get $x^2+4x-25=0$
We get $x=\frac{(-4\pm \sqrt{116})}{2}=2\pm \sqrt{29}$
Since $y^2$ is always positive $4x$ should be also positive , which implies $x\ne 2-\sqrt{29}$
Therefore $x=2+\sqrt{29}$ and for one value of $x$ , we get two values of $y$.
So, the number of points at which two equations intersect is $2$.