How many points of intersection are between the graphs of the equations $x^{2} + y^{2} = 7$ and $x^{2} - y^{2} = 1$ ?

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Solution

The correct option is E $4$
Given $x^{2} + y^{2} = 7$ and $x^{2} - y^{2} = 1$
Add two equations, we get $2 x^{2} = 8$ , which implies $x^{2} = 4$
Therefore $x = \pm 2$ , we get $y = \pm \sqrt{3}$
So, number of solutions is $4$ .

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How many points of intersection are between the graphs of the equations x2+y2=7 and x2−y2=1?

The correct option is E 4Given x2+y2=7 and x2−y2=1Add two equations, we get 2x2=8 , which implies x2=4Therefore x=±2 , we get y=±√3So, number of solutions is 4.

How many points of intersection are between the graphs of the equations $x^{2} + y^{2} = 7$ and $x^{2} - y^{2} = 1$ ?

The correct option is E $4$
Given $x^{2} + y^{2} = 7$ and $x^{2} - y^{2} = 1$
Add two equations, we get $2 x^{2} = 8$ , which implies $x^{2} = 4$
Therefore $x = \pm 2$ , we get $y = \pm \sqrt{3}$
So, number of solutions is $4$ .